(x+8)(2x+1)/2=90

Solution for (x+8)(2x+1)/2=90 equation:

(x+8)(2x+1)/2=90

We move all terms to the left:

(x+8)(2x+1)/2-(90)=0

We multiply parentheses ..

(+2x^2+x+16x+8)/2-90=0

We multiply all the terms by the denominator


(+2x^2+x+16x+8)-90*2=0

We add all the numbers together, and all the variables

(+2x^2+x+16x+8)-180=0

We get rid of parentheses

2x^2+x+16x+8-180=0

We add all the numbers together, and all the variables

2x^2+17x-172=0

a = 2; b = 17; c = -172;
Δ = b2-4ac
Δ = 172-4·2·(-172)
Δ = 1665
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:

$\sqrt{\Delta}=\sqrt{1665}=\sqrt{9*185}=\sqrt{9}*\sqrt{185}=3\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3\sqrt{185}}{2*2}=\frac{-17-3\sqrt{185}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3\sqrt{185}}{2*2}=\frac{-17+3\sqrt{185}}{4}
$