1064=(20+x)*(30+x)

Solution for 1064=(20+x)*(30+x) equation:

1064=(20+x)(30+x)

We move all terms to the left:

1064-((20+x)(30+x))=0

We add all the numbers together, and all the variables

-((x+20)(x+30))+1064=0

We multiply parentheses ..

-((+x^2+30x+20x+600))+1064=0


We calculate terms in parentheses: -((+x^2+30x+20x+600)), so:

(+x^2+30x+20x+600)

We get rid of parentheses

x^2+30x+20x+600

We add all the numbers together, and all the variables

x^2+50x+600

Back to the equation:

-(x^2+50x+600)


We get rid of parentheses

-x^2-50x-600+1064=0

We add all the numbers together, and all the variables

-1x^2-50x+464=0

a = -1; b = -50; c = +464;
Δ = b2-4ac
Δ = -502-4·(-1)·464
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-66}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+66}{2*-1}=\frac{116}{-2}
=-58
$