(4+x)(x+5)=90

Solution for (4+x)(x+5)=90 equation:

(4+x)(x+5)=90

We move all terms to the left:

(4+x)(x+5)-(90)=0

We add all the numbers together, and all the variables

(x+4)(x+5)-90=0

We multiply parentheses ..

(+x^2+5x+4x+20)-90=0

We get rid of parentheses

x^2+5x+4x+20-90=0

We add all the numbers together, and all the variables

x^2+9x-70=0

a = 1; b = 9; c = -70;
Δ = b2-4ac
Δ = 92-4·1·(-70)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-19}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+19}{2*1}=\frac{10}{2}
=5
$