(x+50)(4x)=90

Solution for (x+50)(4x)=90 equation:

(x+50)(4x)=90

We move all terms to the left:

(x+50)(4x)-(90)=0

We multiply parentheses

4x^2+200x-90=0

a = 4; b = 200; c = -90;
Δ = b2-4ac
Δ = 2002-4·4·(-90)
Δ = 41440
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:

$\sqrt{\Delta}=\sqrt{41440}=\sqrt{16*2590}=\sqrt{16}*\sqrt{2590}=4\sqrt{2590}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-4\sqrt{2590}}{2*4}=\frac{-200-4\sqrt{2590}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+4\sqrt{2590}}{2*4}=\frac{-200+4\sqrt{2590}}{8}
$