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

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

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

We move all terms to the left:

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

We multiply parentheses

3x-(2(x-5)x)-15=0


We calculate terms in parentheses: -(2(x-5)x), so:

2(x-5)x

We multiply parentheses

2x^2-10x

Back to the equation:

-(2x^2-10x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+13x-15=0

a = -2; b = 13; c = -15;
Δ = b2-4ac
Δ = 132-4·(-2)·(-15)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*-2}=\frac{-6}{-4}
=1+1/2
$