(8x+1)(5x-2)=90

Solution for (8x+1)(5x-2)=90 equation:

(8x+1)(5x-2)=90

We move all terms to the left:

(8x+1)(5x-2)-(90)=0

We multiply parentheses ..

(+40x^2-16x+5x-2)-90=0

We get rid of parentheses

40x^2-16x+5x-2-90=0

We add all the numbers together, and all the variables

40x^2-11x-92=0

a = 40; b = -11; c = -92;
Δ = b2-4ac
Δ = -112-4·40·(-92)
Δ = 14841
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:

$\sqrt{\Delta}=\sqrt{14841}=\sqrt{9*1649}=\sqrt{9}*\sqrt{1649}=3\sqrt{1649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{1649}}{2*40}=\frac{11-3\sqrt{1649}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{1649}}{2*40}=\frac{11+3\sqrt{1649}}{80}
$