How do you solve 2x^2 = 14x + 20 using the quadratic formula?

Apr 23, 2016

${x}_{1} = - 1 , 22$
${x}_{2} = 8 , 22$

Explanation:

$2 {x}^{2} = 14 x + 20$
$2 {x}^{2} - 14 x - 20 = 0$
$2 \left({x}^{2} - 7 x - 10\right) = 0$
${x}^{2} - 7 x - 10 = 0$

$a {x}^{2} + b x + c = 0$
$a = 1 \text{ ; "b=-7" ; } c = - 10$

$\Delta = \sqrt{{b}^{2} - 4 \cdot a \cdot c}$

$\Delta = \sqrt{49 + 4 \cdot 1 \cdot 10}$

$\Delta = \sqrt{89}$

$\Delta = 9 , 43$

${x}_{1} = \frac{- b - \Delta}{2 \cdot a}$

${x}_{1} = \frac{7 - 9 , 43}{2}$

${x}_{1} = - 1 , 22$

${x}_{2} = \frac{- b + \Delta}{2 \cdot a}$

${x}_{2} = \frac{7 + 9 , 43}{2}$

${x}_{2} = 8 , 22$