(5x+1)(4x+8)=90

Solution for (5x+1)(4x+8)=90 equation:

(5x+1)(4x+8)=90

We move all terms to the left:

(5x+1)(4x+8)-(90)=0

We multiply parentheses ..

(+20x^2+40x+4x+8)-90=0

We get rid of parentheses

20x^2+40x+4x+8-90=0

We add all the numbers together, and all the variables

20x^2+44x-82=0

a = 20; b = 44; c = -82;
Δ = b2-4ac
Δ = 442-4·20·(-82)
Δ = 8496
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:

$\sqrt{\Delta}=\sqrt{8496}=\sqrt{144*59}=\sqrt{144}*\sqrt{59}=12\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-12\sqrt{59}}{2*20}=\frac{-44-12\sqrt{59}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+12\sqrt{59}}{2*20}=\frac{-44+12\sqrt{59}}{40}
$