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

Solution for 3x(x-5)=5(15-3x) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(5(-3x+15)), so:

5(-3x+15)

We multiply parentheses

-15x+75

Back to the equation:

-(-15x+75)


We get rid of parentheses

3x^2-15x+15x-75=0

We add all the numbers together, and all the variables

3x^2-75=0

a = 3; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·3·(-75)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*3}=\frac{30}{6}
=5
$