X^2+41x+4=90

Solution for X^2+41x+4=90 equation:

X^2+41X+4=90

We move all terms to the left:

X^2+41X+4-(90)=0

We add all the numbers together, and all the variables

X^2+41X-86=0

a = 1; b = 41; c = -86;
Δ = b2-4ac
Δ = 412-4·1·(-86)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-45}{2*1}=\frac{-86}{2}
=-43
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+45}{2*1}=\frac{4}{2}
=2
$