x^2+40+23x=90

Solution for x^2+40+23x=90 equation:

x^2+40+23x=90

We move all terms to the left:

x^2+40+23x-(90)=0

We add all the numbers together, and all the variables

x^2+23x-50=0

a = 1; b = 23; c = -50;
Δ = b2-4ac
Δ = 232-4·1·(-50)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-27}{2*1}=\frac{-50}{2}
=-25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+27}{2*1}=\frac{4}{2}
=2
$