6x^2+4x=24

Solution for 6x^2+4x=24 equation:

6x^2+4x=24

We move all terms to the left:

6x^2+4x-(24)=0

a = 6; b = 4; c = -24;
Δ = b2-4ac
Δ = 42-4·6·(-24)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{37}}{2*6}=\frac{-4-4\sqrt{37}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{37}}{2*6}=\frac{-4+4\sqrt{37}}{12}
$