(40-x)(30-x)=550

Solution for (40-x)(30-x)=550 equation:

(40-x)(30-x)=550

We move all terms to the left:

(40-x)(30-x)-(550)=0

We add all the numbers together, and all the variables

(-1x+40)(-1x+30)-550=0

We multiply parentheses ..

(+x^2-30x-40x+1200)-550=0

We get rid of parentheses

x^2-30x-40x+1200-550=0

We add all the numbers together, and all the variables

x^2-70x+650=0

a = 1; b = -70; c = +650;
Δ = b2-4ac
Δ = -702-4·1·650
Δ = 2300
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:

$\sqrt{\Delta}=\sqrt{2300}=\sqrt{100*23}=\sqrt{100}*\sqrt{23}=10\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-10\sqrt{23}}{2*1}=\frac{70-10\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+10\sqrt{23}}{2*1}=\frac{70+10\sqrt{23}}{2}
$