(x+5)(x+10)=374

Solution for (x+5)(x+10)=374 equation:

(x+5)(x+10)=374

We move all terms to the left:

(x+5)(x+10)-(374)=0

We multiply parentheses ..

(+x^2+10x+5x+50)-374=0

We get rid of parentheses

x^2+10x+5x+50-374=0

We add all the numbers together, and all the variables

x^2+15x-324=0

a = 1; b = 15; c = -324;
Δ = b2-4ac
Δ = 152-4·1·(-324)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-39}{2*1}=\frac{-54}{2}
=-27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+39}{2*1}=\frac{24}{2}
=12
$