2x(x-48)=180

Solution for 2x(x-48)=180 equation:

2x(x-48)=180

We move all terms to the left:

2x(x-48)-(180)=0

We multiply parentheses

2x^2-96x-180=0

a = 2; b = -96; c = -180;
Δ = b2-4ac
Δ = -962-4·2·(-180)
Δ = 10656
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:

$\sqrt{\Delta}=\sqrt{10656}=\sqrt{144*74}=\sqrt{144}*\sqrt{74}=12\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-12\sqrt{74}}{2*2}=\frac{96-12\sqrt{74}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+12\sqrt{74}}{2*2}=\frac{96+12\sqrt{74}}{4}
$