(5x+25)(x-8)=60(x+5)

Solution for (5x+25)(x-8)=60(x+5) equation:

(5x+25)(x-8)=60(x+5)

We move all terms to the left:

(5x+25)(x-8)-(60(x+5))=0

We multiply parentheses ..

(+5x^2-40x+25x-200)-(60(x+5))=0


We calculate terms in parentheses: -(60(x+5)), so:

60(x+5)

We multiply parentheses

60x+300

Back to the equation:

-(60x+300)


We get rid of parentheses

5x^2-40x+25x-60x-200-300=0

We add all the numbers together, and all the variables

5x^2-75x-500=0

a = 5; b = -75; c = -500;
Δ = b2-4ac
Δ = -752-4·5·(-500)
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-125}{2*5}=\frac{-50}{10}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+125}{2*5}=\frac{200}{10}
=20
$