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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+x^2+2x-1x-2)-90=0

We get rid of parentheses

x^2+2x-1x-2-90=0

We add all the numbers together, and all the variables

x^2+x-92=0

a = 1; b = 1; c = -92;
Δ = b2-4ac
Δ = 12-4·1·(-92)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{41}}{2*1}=\frac{-1-3\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{41}}{2*1}=\frac{-1+3\sqrt{41}}{2}
$