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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -((2x+3)x), so:

(2x+3)x

We multiply parentheses

2x^2+3x

Back to the equation:

-(2x^2+3x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-2x=0

a = -2; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-2)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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