5x(2x-7)=8

Solution for 5x(2x-7)=8 equation:

5x(2x-7)=8

We move all terms to the left:

5x(2x-7)-(8)=0

We multiply parentheses

10x^2-35x-8=0

a = 10; b = -35; c = -8;
Δ = b2-4ac
Δ = -352-4·10·(-8)
Δ = 1545
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{-(-35)-\sqrt{1545}}{2*10}=\frac{35-\sqrt{1545}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1545}}{2*10}=\frac{35+\sqrt{1545}}{20}
$