40x(x-2)=6x-8

Solution for 40x(x-2)=6x-8 equation:

40x(x-2)=6x-8

We move all terms to the left:

40x(x-2)-(6x-8)=0

We multiply parentheses

40x^2-80x-(6x-8)=0

We get rid of parentheses

40x^2-80x-6x+8=0

We add all the numbers together, and all the variables

40x^2-86x+8=0

a = 40; b = -86; c = +8;
Δ = b2-4ac
Δ = -862-4·40·8
Δ = 6116
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:

$\sqrt{\Delta}=\sqrt{6116}=\sqrt{4*1529}=\sqrt{4}*\sqrt{1529}=2\sqrt{1529}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-2\sqrt{1529}}{2*40}=\frac{86-2\sqrt{1529}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+2\sqrt{1529}}{2*40}=\frac{86+2\sqrt{1529}}{80}
$