4x(8-5x)=7

Solution for 4x(8-5x)=7 equation:

4x(8-5x)=7

We move all terms to the left:

4x(8-5x)-(7)=0

We add all the numbers together, and all the variables

4x(-5x+8)-7=0

We multiply parentheses

-20x^2+32x-7=0

a = -20; b = 32; c = -7;
Δ = b2-4ac
Δ = 322-4·(-20)·(-7)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{29}}{2*-20}=\frac{-32-4\sqrt{29}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{29}}{2*-20}=\frac{-32+4\sqrt{29}}{-40}
$