12x^2+8x=13

Solution for 12x^2+8x=13 equation:

12x^2+8x=13

We move all terms to the left:

12x^2+8x-(13)=0

a = 12; b = 8; c = -13;
Δ = b2-4ac
Δ = 82-4·12·(-13)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{43}}{2*12}=\frac{-8-4\sqrt{43}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{43}}{2*12}=\frac{-8+4\sqrt{43}}{24}
$