1000=(25+2x)(20+2x)

Solution for 1000=(25+2x)(20+2x) equation:

1000=(25+2x)(20+2x)

We move all terms to the left:

1000-((25+2x)(20+2x))=0

We add all the numbers together, and all the variables

-((2x+25)(2x+20))+1000=0

We multiply parentheses ..

-((+4x^2+40x+50x+500))+1000=0


We calculate terms in parentheses: -((+4x^2+40x+50x+500)), so:

(+4x^2+40x+50x+500)

We get rid of parentheses

4x^2+40x+50x+500

We add all the numbers together, and all the variables

4x^2+90x+500

Back to the equation:

-(4x^2+90x+500)


We get rid of parentheses

-4x^2-90x-500+1000=0

We add all the numbers together, and all the variables

-4x^2-90x+500=0

a = -4; b = -90; c = +500;
Δ = b2-4ac
Δ = -902-4·(-4)·500
Δ = 16100
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:

$\sqrt{\Delta}=\sqrt{16100}=\sqrt{100*161}=\sqrt{100}*\sqrt{161}=10\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10\sqrt{161}}{2*-4}=\frac{90-10\sqrt{161}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10\sqrt{161}}{2*-4}=\frac{90+10\sqrt{161}}{-8}
$