6x(x-3)=5(x-3)

Solution for 6x(x-3)=5(x-3) equation:

6x(x-3)=5(x-3)

We move all terms to the left:

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

We multiply parentheses

6x^2-18x-(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

6x^2-18x-5x+15=0

We add all the numbers together, and all the variables

6x^2-23x+15=0

a = 6; b = -23; c = +15;
Δ = b2-4ac
Δ = -232-4·6·15
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-13}{2*6}=\frac{10}{12}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+13}{2*6}=\frac{36}{12}
=3
$