(x-5)*(x+30)=25*(x+10)

Solution for (x-5)*(x+30)=25*(x+10) equation:

(x-5)(x+30)=25(x+10)

We move all terms to the left:

(x-5)(x+30)-(25(x+10))=0

We multiply parentheses ..

(+x^2+30x-5x-150)-(25(x+10))=0


We calculate terms in parentheses: -(25(x+10)), so:

25(x+10)

We multiply parentheses

25x+250

Back to the equation:

-(25x+250)


We get rid of parentheses

x^2+30x-5x-25x-150-250=0

We add all the numbers together, and all the variables

x^2-400=0

a = 1; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·1·(-400)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*1}=\frac{40}{2}
=20
$