(5x+3)(8x-4)=90

Solution for (5x+3)(8x-4)=90 equation:

(5x+3)(8x-4)=90

We move all terms to the left:

(5x+3)(8x-4)-(90)=0

We multiply parentheses ..

(+40x^2-20x+24x-12)-90=0

We get rid of parentheses

40x^2-20x+24x-12-90=0

We add all the numbers together, and all the variables

40x^2+4x-102=0

a = 40; b = 4; c = -102;
Δ = b2-4ac
Δ = 42-4·40·(-102)
Δ = 16336
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:

$\sqrt{\Delta}=\sqrt{16336}=\sqrt{16*1021}=\sqrt{16}*\sqrt{1021}=4\sqrt{1021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{1021}}{2*40}=\frac{-4-4\sqrt{1021}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{1021}}{2*40}=\frac{-4+4\sqrt{1021}}{80}
$