25x(x+5)=20(1.5x+1)

Solution for 25x(x+5)=20(1.5x+1) equation:

25x(x+5)=20(1.5x+1)

We move all terms to the left:

25x(x+5)-(20(1.5x+1))=0

We multiply parentheses

25x^2+125x-(20(1.5x+1))=0


We calculate terms in parentheses: -(20(1.5x+1)), so:

20(1.5x+1)

We multiply parentheses

20x+20

Back to the equation:

-(20x+20)


We get rid of parentheses

25x^2+125x-20x-20=0

We add all the numbers together, and all the variables

25x^2+105x-20=0

a = 25; b = 105; c = -20;
Δ = b2-4ac
Δ = 1052-4·25·(-20)
Δ = 13025
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:

$\sqrt{\Delta}=\sqrt{13025}=\sqrt{25*521}=\sqrt{25}*\sqrt{521}=5\sqrt{521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-5\sqrt{521}}{2*25}=\frac{-105-5\sqrt{521}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+5\sqrt{521}}{2*25}=\frac{-105+5\sqrt{521}}{50}
$