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

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

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

We move all terms to the left:

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

We multiply parentheses

25x-((x+30)(x-5))+250=0

We multiply parentheses ..

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


We calculate terms in parentheses: -((+x^2-5x+30x-150)), so:

(+x^2-5x+30x-150)

We get rid of parentheses

x^2-5x+30x-150

We add all the numbers together, and all the variables

x^2+25x-150

Back to the equation:

-(x^2+25x-150)


We add all the numbers together, and all the variables

25x-(x^2+25x-150)+250=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^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
$