x(8x-4)=40

Solution for x(8x-4)=40 equation:

x(8x-4)=40

We move all terms to the left:

x(8x-4)-(40)=0

We multiply parentheses

8x^2-4x-40=0

a = 8; b = -4; c = -40;
Δ = b2-4ac
Δ = -42-4·8·(-40)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-36}{2*8}=\frac{-32}{16}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+36}{2*8}=\frac{40}{16}
=2+1/2
$