x(25+x)=224

Solution for x(25+x)=224 equation:

x(25+x)=224

We move all terms to the left:

x(25+x)-(224)=0

We add all the numbers together, and all the variables

x(x+25)-224=0

We multiply parentheses

x^2+25x-224=0

a = 1; b = 25; c = -224;
Δ = b2-4ac
Δ = 252-4·1·(-224)
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{-(25)-39}{2*1}=\frac{-64}{2}
=-32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+39}{2*1}=\frac{14}{2}
=7
$