(x+5)(x+10)-1050=0

Solution for (x+5)(x+10)-1050=0 equation:

(x+5)(x+10)-1050=0

We multiply parentheses ..

(+x^2+10x+5x+50)-1050=0

We get rid of parentheses

x^2+10x+5x+50-1050=0

We add all the numbers together, and all the variables

x^2+15x-1000=0

a = 1; b = 15; c = -1000;
Δ = b2-4ac
Δ = 152-4·1·(-1000)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-65}{2*1}=\frac{-80}{2}
=-40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+65}{2*1}=\frac{50}{2}
=25
$