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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

2x^2-3x+3x-8=0

We add all the numbers together, and all the variables

2x^2-8=0

a = 2; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·2·(-8)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*2}=\frac{8}{4}
=2
$