65+(x-5)x=180

Solution for 65+(x-5)x=180 equation:

65+(x-5)x=180

We move all terms to the left:

65+(x-5)x-(180)=0

We add all the numbers together, and all the variables

(x-5)x-115=0

We multiply parentheses

x^2-5x-115=0

a = 1; b = -5; c = -115;
Δ = b2-4ac
Δ = -52-4·1·(-115)
Δ = 485
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{485}}{2*1}=\frac{5-\sqrt{485}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{485}}{2*1}=\frac{5+\sqrt{485}}{2}
$