x(8x-27)=20

Solution for x(8x-27)=20 equation:

x(8x-27)=20

We move all terms to the left:

x(8x-27)-(20)=0

We multiply parentheses

8x^2-27x-20=0

a = 8; b = -27; c = -20;
Δ = b2-4ac
Δ = -272-4·8·(-20)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-37}{2*8}=\frac{-10}{16}
=-5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+37}{2*8}=\frac{64}{16}
=4
$