(20+x)(50+x)=2275

Solution for (20+x)(50+x)=2275 equation:

(20+x)(50+x)=2275

We move all terms to the left:

(20+x)(50+x)-(2275)=0

We add all the numbers together, and all the variables

(x+20)(x+50)-2275=0

We multiply parentheses ..

(+x^2+50x+20x+1000)-2275=0

We get rid of parentheses

x^2+50x+20x+1000-2275=0

We add all the numbers together, and all the variables

x^2+70x-1275=0

a = 1; b = 70; c = -1275;
Δ = b2-4ac
Δ = 702-4·1·(-1275)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-100}{2*1}=\frac{-170}{2}
=-85
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+100}{2*1}=\frac{30}{2}
=15
$