(20+x)(x-30)=230

Solution for (20+x)(x-30)=230 equation:

(20+x)(x-30)=230

We move all terms to the left:

(20+x)(x-30)-(230)=0

We add all the numbers together, and all the variables

(x+20)(x-30)-230=0

We multiply parentheses ..

(+x^2-30x+20x-600)-230=0

We get rid of parentheses

x^2-30x+20x-600-230=0

We add all the numbers together, and all the variables

x^2-10x-830=0

a = 1; b = -10; c = -830;
Δ = b2-4ac
Δ = -102-4·1·(-830)
Δ = 3420
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:

$\sqrt{\Delta}=\sqrt{3420}=\sqrt{36*95}=\sqrt{36}*\sqrt{95}=6\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{95}}{2*1}=\frac{10-6\sqrt{95}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{95}}{2*1}=\frac{10+6\sqrt{95}}{2}
$