(10+x)(24+x)=480

Solution for (10+x)(24+x)=480 equation:

(10+x)(24+x)=480

We move all terms to the left:

(10+x)(24+x)-(480)=0

We add all the numbers together, and all the variables

(x+10)(x+24)-480=0

We multiply parentheses ..

(+x^2+24x+10x+240)-480=0

We get rid of parentheses

x^2+24x+10x+240-480=0

We add all the numbers together, and all the variables

x^2+34x-240=0

a = 1; b = 34; c = -240;
Δ = b2-4ac
Δ = 342-4·1·(-240)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-46}{2*1}=\frac{-80}{2}
=-40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+46}{2*1}=\frac{12}{2}
=6
$