(2x+3)(5x-4)=8

Solution for (2x+3)(5x-4)=8 equation:

(2x+3)(5x-4)=8

We move all terms to the left:

(2x+3)(5x-4)-(8)=0

We multiply parentheses ..

(+10x^2-8x+15x-12)-8=0

We get rid of parentheses

10x^2-8x+15x-12-8=0

We add all the numbers together, and all the variables

10x^2+7x-20=0

a = 10; b = 7; c = -20;
Δ = b2-4ac
Δ = 72-4·10·(-20)
Δ = 849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{849}}{2*10}=\frac{-7-\sqrt{849}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{849}}{2*10}=\frac{-7+\sqrt{849}}{20}
$