8-5x(x-4)=2x-6

Solution for 8-5x(x-4)=2x-6 equation:

8-5x(x-4)=2x-6

We move all terms to the left:

8-5x(x-4)-(2x-6)=0

We multiply parentheses

-5x^2+20x-(2x-6)+8=0

We get rid of parentheses

-5x^2+20x-2x+6+8=0

We add all the numbers together, and all the variables

-5x^2+18x+14=0

a = -5; b = 18; c = +14;
Δ = b2-4ac
Δ = 182-4·(-5)·14
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{151}}{2*-5}=\frac{-18-2\sqrt{151}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{151}}{2*-5}=\frac{-18+2\sqrt{151}}{-10}
$