7x^2-12=-17x

Solution for 7x^2-12=-17x equation:

7x^2-12=-17x

We move all terms to the left:

7x^2-12-(-17x)=0

We get rid of parentheses

7x^2+17x-12=0

a = 7; b = 17; c = -12;
Δ = b2-4ac
Δ = 172-4·7·(-12)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-25}{2*7}=\frac{-42}{14}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+25}{2*7}=\frac{8}{14}
=4/7
$