# How do you solve 8x-10=x^2-7x+3 using the quadratic formula?

Aug 24, 2017

Convert the given equation into standard quadratic form and then apply the quadratic formula to get
$\textcolor{w h i t e}{\text{XXX}} x = \frac{15 \pm \sqrt{173}}{2}$

#### Explanation:

$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} {x}^{2} + \textcolor{b l u e}{b} x + \textcolor{g r e e n}{c} = 0$
with solutions given by the quadratic formula
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - 4 \textcolor{red}{a} \textcolor{g r e e n}{c}}}{2 \textcolor{red}{a}}$

Converting the given equation:
$\textcolor{w h i t e}{\text{XXX}} 8 x - 10 = {x}^{2} - 7 x + 3$
into standard form results in
$\textcolor{w h i t e}{\text{XXX")color(red)1x^2+color(blue)(} \left(- 15\right)} x + \textcolor{g r e e n}{13} = 0$

Plugging the coefficient values into the quadratic formula gives the result shown in the answer above.

Aug 24, 2017

Answers(to 3 d.p.): 0.924 and 14.077

#### Explanation:

Since you have

$8 x - 10 =$${x}^{2} - 7 x + 3$,

You transfer the numbers on the left hand side to the right in order to get the normal order: ax^2 ± bx ± c.

$8 x - 10 =$${x}^{2} - 7 x + 3$

If you add 10 on both sides, you eliminate the -10 on the left and bring it to the right.

$8 x - 10 + 10 =$${x}^{2} - 7 x + 3 + 10$

= $8 x =$${x}^{2} - 7 x + 13$

Do the same for the 8x until you get 0.

$8 x - 8 x =$${x}^{2} - 7 x + 13 - 8 x$

= $0 =$${x}^{2} - 15 x + 13$

= ${x}^{2} - 15 x + 13$

So now that you have everything in order, you can input the coefficients into the quadratic formula:

x=(-(-15) ± sqrt(225 - 52))/(2×1)

=(15 ± sqrt(173))/(2×1)

=(15 ± sqrt(173))/2

$= \frac{15 + \sqrt{173}}{2}$

$= 14.077$

$= \frac{15 - \sqrt{173}}{2}$

$= 0.924$

Hope this helps!