(18+x)(35+x)=1260

Solution for (18+x)(35+x)=1260 equation:

(18+x)(35+x)=1260

We move all terms to the left:

(18+x)(35+x)-(1260)=0

We add all the numbers together, and all the variables

(x+18)(x+35)-1260=0

We multiply parentheses ..

(+x^2+35x+18x+630)-1260=0

We get rid of parentheses

x^2+35x+18x+630-1260=0

We add all the numbers together, and all the variables

x^2+53x-630=0

a = 1; b = 53; c = -630;
Δ = b2-4ac
Δ = 532-4·1·(-630)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-73}{2*1}=\frac{-126}{2}
=-63
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+73}{2*1}=\frac{20}{2}
=10
$