704=(10+2X)(20+2x)-30

Solution for 704=(10+2X)(20+2x)-30 equation:

704=(10+2X)(20+2X)-30

We move all terms to the left:

704-((10+2X)(20+2X)-30)=0

We add all the numbers together, and all the variables

-((2X+10)(2X+20)-30)+704=0

We multiply parentheses ..

-((+4X^2+40X+20X+200)-30)+704=0


We calculate terms in parentheses: -((+4X^2+40X+20X+200)-30), so:

(+4X^2+40X+20X+200)-30

We get rid of parentheses

4X^2+40X+20X+200-30

We add all the numbers together, and all the variables

4X^2+60X+170

Back to the equation:

-(4X^2+60X+170)


We get rid of parentheses

-4X^2-60X-170+704=0

We add all the numbers together, and all the variables

-4X^2-60X+534=0

a = -4; b = -60; c = +534;
Δ = b2-4ac
Δ = -602-4·(-4)·534
Δ = 12144
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:

$\sqrt{\Delta}=\sqrt{12144}=\sqrt{16*759}=\sqrt{16}*\sqrt{759}=4\sqrt{759}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{759}}{2*-4}=\frac{60-4\sqrt{759}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{759}}{2*-4}=\frac{60+4\sqrt{759}}{-8}
$