x^2=180(x-2)

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

x^2=180(x-2)

We move all terms to the left:

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


We calculate terms in parentheses: -(180(x-2)), so:

180(x-2)

We multiply parentheses

180x-360

Back to the equation:

-(180x-360)


We get rid of parentheses

x^2-180x+360=0

a = 1; b = -180; c = +360;
Δ = b2-4ac
Δ = -1802-4·1·360
Δ = 30960
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:

$\sqrt{\Delta}=\sqrt{30960}=\sqrt{144*215}=\sqrt{144}*\sqrt{215}=12\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-12\sqrt{215}}{2*1}=\frac{180-12\sqrt{215}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+12\sqrt{215}}{2*1}=\frac{180+12\sqrt{215}}{2}
$