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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

2(2x-3)

We multiply parentheses

4x-6

Back to the equation:

-(4x-6)


We get rid of parentheses

10x^2-15x-4x+6=0

We add all the numbers together, and all the variables

10x^2-19x+6=0

a = 10; b = -19; c = +6;
Δ = b2-4ac
Δ = -192-4·10·6
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-11}{2*10}=\frac{8}{20}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+11}{2*10}=\frac{30}{20}
=1+1/2
$