# How do you solve 35x^2+6x-9=0  using the quadratic formula?

Apr 23, 2016

${x}_{1} = - \frac{6}{10}$
${x}_{2} = \frac{3}{7}$

#### Explanation:

"if an equation is given as "ax^2+bx+c=0;
"the quadratic formula is determined b y "x_"1,2"=(-b±sqrt(b^2-4*a*c))/(2*a)

$35 {x}^{2} + 6 x - 9 = 0$
$a = 35 \text{ ;"b=6" ;} c = - 9$

$\Delta = \sqrt{{b}^{2} - 4 \cdot a \cdot c} = \sqrt{{6}^{2} + 4 \cdot 35 \cdot 9}$
$\Delta = \sqrt{36 + 1260} = \sqrt{1296}$
$\Delta = 36$

${x}_{1} = \frac{- b - \Delta}{2 \cdot a} \text{ "x_1=(-6-36)/(2*35)" } {x}_{1} = - \frac{42}{70}$

${x}_{1} = - \frac{6}{10}$

${x}_{2} = \frac{- b + \Delta}{2 \cdot a} \text{ "x_2=(-6+36)/(2*35)" "x_2=30/70" } {x}_{2} = \frac{3}{7}$