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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(3(2x-5)), so:

3(2x-5)

We multiply parentheses

6x-15

Back to the equation:

-(6x-15)


We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2-21x+15=0

a = 5; b = -21; c = +15;
Δ = b2-4ac
Δ = -212-4·5·15
Δ = 141
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{141}}{2*5}=\frac{21-\sqrt{141}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{141}}{2*5}=\frac{21+\sqrt{141}}{10}
$