-12x^2=-17x-5

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

-12x^2=-17x-5

We move all terms to the left:

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

We get rid of parentheses

-12x^2+17x+5=0

a = -12; b = 17; c = +5;
Δ = b2-4ac
Δ = 172-4·(-12)·5
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*-12}=\frac{-40}{-24}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+23}{2*-12}=\frac{6}{-24}
=-1/4
$