x*(x+43)=90

Solution for x*(x+43)=90 equation:

x(x+43)=90

We move all terms to the left:

x(x+43)-(90)=0

We multiply parentheses

x^2+43x-90=0

a = 1; b = 43; c = -90;
Δ = b2-4ac
Δ = 432-4·1·(-90)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-47}{2*1}=\frac{-90}{2}
=-45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+47}{2*1}=\frac{4}{2}
=2
$