-17x+6=12x^2

Solution for -17x+6=12x^2 equation:

-17x+6=12x^2

We move all terms to the left:

-17x+6-(12x^2)=0

determiningTheFunctionDomain
-12x^2-17x+6=0

a = -12; b = -17; c = +6;
Δ = b2-4ac
Δ = -172-4·(-12)·6
Δ = 577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{577}}{2*-12}=\frac{17-\sqrt{577}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{577}}{2*-12}=\frac{17+\sqrt{577}}{-24}
$