(60+x)(100+x)=18000

Solution for (60+x)(100+x)=18000 equation:

(60+x)(100+x)=18000

We move all terms to the left:

(60+x)(100+x)-(18000)=0

We add all the numbers together, and all the variables

(x+60)(x+100)-18000=0

We multiply parentheses ..

(+x^2+100x+60x+6000)-18000=0

We get rid of parentheses

x^2+100x+60x+6000-18000=0

We add all the numbers together, and all the variables

x^2+160x-12000=0

a = 1; b = 160; c = -12000;
Δ = b2-4ac
Δ = 1602-4·1·(-12000)
Δ = 73600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{73600}=\sqrt{1600*46}=\sqrt{1600}*\sqrt{46}=40\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-40\sqrt{46}}{2*1}=\frac{-160-40\sqrt{46}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+40\sqrt{46}}{2*1}=\frac{-160+40\sqrt{46}}{2}
$