6x2=4x+48=360

Solution for 6x2=4x+48=360 equation:

6x^2=4x+48=360

We move all terms to the left:

6x^2-(4x+48)=0

We get rid of parentheses

6x^2-4x-48=0

a = 6; b = -4; c = -48;
Δ = b2-4ac
Δ = -42-4·6·(-48)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{73}}{2*6}=\frac{4-4\sqrt{73}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{73}}{2*6}=\frac{4+4\sqrt{73}}{12}
$