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

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

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

We move all terms to the left:

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

We multiply parentheses

10x^2-15x-(-2x+3)=0

We get rid of parentheses

10x^2-15x+2x-3=0

We add all the numbers together, and all the variables

10x^2-13x-3=0

a = 10; b = -13; c = -3;
Δ = b2-4ac
Δ = -132-4·10·(-3)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*10}=\frac{-4}{20}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*10}=\frac{30}{20}
=1+1/2
$