90+(2x+1)(5x-50)=180

Solution for 90+(2x+1)(5x-50)=180 equation:

90+(2x+1)(5x-50)=180

We move all terms to the left:

90+(2x+1)(5x-50)-(180)=0

We add all the numbers together, and all the variables

(2x+1)(5x-50)-90=0

We multiply parentheses ..

(+10x^2-100x+5x-50)-90=0

We get rid of parentheses

10x^2-100x+5x-50-90=0

We add all the numbers together, and all the variables

10x^2-95x-140=0

a = 10; b = -95; c = -140;
Δ = b2-4ac
Δ = -952-4·10·(-140)
Δ = 14625
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:

$\sqrt{\Delta}=\sqrt{14625}=\sqrt{225*65}=\sqrt{225}*\sqrt{65}=15\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-15\sqrt{65}}{2*10}=\frac{95-15\sqrt{65}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+15\sqrt{65}}{2*10}=\frac{95+15\sqrt{65}}{20}
$