X(x+1)+(2x+5)(x-1)=90

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

X(X+1)+(2X+5)(X-1)=90

We move all terms to the left:

X(X+1)+(2X+5)(X-1)-(90)=0

We multiply parentheses

X^2+X+(2X+5)(X-1)-90=0

We multiply parentheses ..

X^2+(+2X^2-2X+5X-5)+X-90=0

We get rid of parentheses

X^2+2X^2-2X+5X+X-5-90=0

We add all the numbers together, and all the variables

3X^2+4X-95=0

a = 3; b = 4; c = -95;
Δ = b2-4ac
Δ = 42-4·3·(-95)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-34}{2*3}=\frac{-38}{6}
=-6+1/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+34}{2*3}=\frac{30}{6}
=5
$