8x(x-2)=4x-10

Solution for 8x(x-2)=4x-10 equation:

8x(x-2)=4x-10

We move all terms to the left:

8x(x-2)-(4x-10)=0

We multiply parentheses

8x^2-16x-(4x-10)=0

We get rid of parentheses

8x^2-16x-4x+10=0

We add all the numbers together, and all the variables

8x^2-20x+10=0

a = 8; b = -20; c = +10;
Δ = b2-4ac
Δ = -202-4·8·10
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{5}}{2*8}=\frac{20-4\sqrt{5}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{5}}{2*8}=\frac{20+4\sqrt{5}}{16}
$