15x^2-4x=12

Solution for 15x^2-4x=12 equation:

15x^2-4x=12

We move all terms to the left:

15x^2-4x-(12)=0

a = 15; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·15·(-12)
Δ = 736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{46}}{2*15}=\frac{4-4\sqrt{46}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{46}}{2*15}=\frac{4+4\sqrt{46}}{30}
$