(2x-17)+(x+53)(x)=180

Solution for (2x-17)+(x+53)(x)=180 equation:

(2x-17)+(x+53)(x)=180

We move all terms to the left:

(2x-17)+(x+53)(x)-(180)=0

We multiply parentheses

x^2+(2x-17)+53x-180=0

We get rid of parentheses

x^2+2x+53x-17-180=0

We add all the numbers together, and all the variables

x^2+55x-197=0

a = 1; b = 55; c = -197;
Δ = b2-4ac
Δ = 552-4·1·(-197)
Δ = 3813
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{-(55)-\sqrt{3813}}{2*1}=\frac{-55-\sqrt{3813}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{3813}}{2*1}=\frac{-55+\sqrt{3813}}{2}
$