3(5x-25)=15x(x-25)

Solution for 3(5x-25)=15x(x-25) equation:

3(5x-25)=15x(x-25)

We move all terms to the left:

3(5x-25)-(15x(x-25))=0

We multiply parentheses

15x-(15x(x-25))-75=0


We calculate terms in parentheses: -(15x(x-25)), so:

15x(x-25)

We multiply parentheses

15x^2-375x

Back to the equation:

-(15x^2-375x)


We get rid of parentheses

-15x^2+15x+375x-75=0

We add all the numbers together, and all the variables

-15x^2+390x-75=0

a = -15; b = 390; c = -75;
Δ = b2-4ac
Δ = 3902-4·(-15)·(-75)
Δ = 147600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{147600}=\sqrt{3600*41}=\sqrt{3600}*\sqrt{41}=60\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(390)-60\sqrt{41}}{2*-15}=\frac{-390-60\sqrt{41}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(390)+60\sqrt{41}}{2*-15}=\frac{-390+60\sqrt{41}}{-30}
$