34x=12x^2-6

Solution for 34x=12x^2-6 equation:

34x=12x^2-6

We move all terms to the left:

34x-(12x^2-6)=0

We get rid of parentheses

-12x^2+34x+6=0

a = -12; b = 34; c = +6;
Δ = b2-4ac
Δ = 342-4·(-12)·6
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-38}{2*-12}=\frac{-72}{-24}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+38}{2*-12}=\frac{4}{-24}
=-1/6
$