6x^2+3x=24

Solution for 6x^2+3x=24 equation:

6x^2+3x=24

We move all terms to the left:

6x^2+3x-(24)=0

a = 6; b = 3; c = -24;
Δ = b2-4ac
Δ = 32-4·6·(-24)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{65}}{2*6}=\frac{-3-3\sqrt{65}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{65}}{2*6}=\frac{-3+3\sqrt{65}}{12}
$