(350+2x)(200+2x)=74664

Solution for (350+2x)(200+2x)=74664 equation:

(350+2x)(200+2x)=74664

We move all terms to the left:

(350+2x)(200+2x)-(74664)=0

We add all the numbers together, and all the variables

(2x+350)(2x+200)-74664=0

We multiply parentheses ..

(+4x^2+400x+700x+70000)-74664=0

We get rid of parentheses

4x^2+400x+700x+70000-74664=0

We add all the numbers together, and all the variables

4x^2+1100x-4664=0

a = 4; b = 1100; c = -4664;
Δ = b2-4ac
Δ = 11002-4·4·(-4664)
Δ = 1284624
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:

$\sqrt{\Delta}=\sqrt{1284624}=\sqrt{144*8921}=\sqrt{144}*\sqrt{8921}=12\sqrt{8921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1100)-12\sqrt{8921}}{2*4}=\frac{-1100-12\sqrt{8921}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1100)+12\sqrt{8921}}{2*4}=\frac{-1100+12\sqrt{8921}}{8}
$