-2x(x-2)-3=3x-8x+7

Solution for -2x(x-2)-3=3x-8x+7 equation:

-2x(x-2)-3=3x-8x+7

We move all terms to the left:

-2x(x-2)-3-(3x-8x+7)=0

We add all the numbers together, and all the variables

-2x(x-2)-(-5x+7)-3=0

We multiply parentheses

-2x^2+4x-(-5x+7)-3=0

We get rid of parentheses

-2x^2+4x+5x-7-3=0

We add all the numbers together, and all the variables

-2x^2+9x-10=0

a = -2; b = 9; c = -10;
Δ = b2-4ac
Δ = 92-4·(-2)·(-10)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*-2}=\frac{-8}{-4}
=+2
$