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

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

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

We move all terms to the left:

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

We multiply parentheses

2x^2-6x-(5(x-3))=0


We calculate terms in parentheses: -(5(x-3)), so:

5(x-3)

We multiply parentheses

5x-15

Back to the equation:

-(5x-15)


We get rid of parentheses

2x^2-6x-5x+15=0

We add all the numbers together, and all the variables

2x^2-11x+15=0

a = 2; b = -11; c = +15;
Δ = b2-4ac
Δ = -112-4·2·15
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{-(-11)-1}{2*2}=\frac{10}{4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*2}=\frac{12}{4}
=3
$