5x^2=48x+18

Solution for 5x^2=48x+18 equation:

5x^2=48x+18

We move all terms to the left:

5x^2-(48x+18)=0

We get rid of parentheses

5x^2-48x-18=0

a = 5; b = -48; c = -18;
Δ = b2-4ac
Δ = -482-4·5·(-18)
Δ = 2664
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:

$\sqrt{\Delta}=\sqrt{2664}=\sqrt{36*74}=\sqrt{36}*\sqrt{74}=6\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-6\sqrt{74}}{2*5}=\frac{48-6\sqrt{74}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+6\sqrt{74}}{2*5}=\frac{48+6\sqrt{74}}{10}
$