48=6x^2-30x

Solution for 48=6x^2-30x equation:

48=6x^2-30x

We move all terms to the left:

48-(6x^2-30x)=0

We get rid of parentheses

-6x^2+30x+48=0

a = -6; b = 30; c = +48;
Δ = b2-4ac
Δ = 302-4·(-6)·48
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{57}}{2*-6}=\frac{-30-6\sqrt{57}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{57}}{2*-6}=\frac{-30+6\sqrt{57}}{-12}
$