8-2x(x-3)=5x

Solution for 8-2x(x-3)=5x equation:

8-2x(x-3)=5x

We move all terms to the left:

8-2x(x-3)-(5x)=0

We add all the numbers together, and all the variables

-5x-2x(x-3)+8=0

We multiply parentheses

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

We add all the numbers together, and all the variables

-2x^2+x+8=0

a = -2; b = 1; c = +8;
Δ = b2-4ac
Δ = 12-4·(-2)·8
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{65}}{2*-2}=\frac{-1-\sqrt{65}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{65}}{2*-2}=\frac{-1+\sqrt{65}}{-4}
$