5x^2-12=-17x

Solution for 5x^2-12=-17x equation:

5x^2-12=-17x

We move all terms to the left:

5x^2-12-(-17x)=0

We get rid of parentheses

5x^2+17x-12=0

a = 5; b = 17; c = -12;
Δ = b2-4ac
Δ = 172-4·5·(-12)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-23}{2*5}=\frac{-40}{10}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+23}{2*5}=\frac{6}{10}
=3/5
$