X=(29,7-2x)(21-2x)+2(29,7-2x)x+2(21-2x)x

Solution for X=(29,7-2x)(21-2x)+2(29,7-2x)x+2(21-2x)x equation:

X=(29.7-2X)(21-2X)+2(29.7-2X)X+2(21-2X)X

We move all terms to the left:

X-((29.7-2X)(21-2X)+2(29.7-2X)X+2(21-2X)X)=0

We add all the numbers together, and all the variables

X-((-2X+29.7)(-2X+21)+2(-2X+29.7)X+2(-2X+21)X)=0

We multiply parentheses ..

-((+4X^2-42X-59.4X+623.7)+2(-2X+29.7)X+2(-2X+21)X)+X=0


We calculate terms in parentheses: -((+4X^2-42X-59.4X+623.7)+2(-2X+29.7)X+2(-2X+21)X), so:

(+4X^2-42X-59.4X+623.7)+2(-2X+29.7)X+2(-2X+21)X

We multiply parentheses

(+4X^2-42X-59.4X+623.7)-4X^2-4X^2+59.4X+42X

We get rid of parentheses

4X^2-4X^2-4X^2-42X-59.4X+59.4X+42X+623.7

We add all the numbers together, and all the variables

-4X^2-15X+623.7-7.105427357601E

We add all the numbers together, and all the variables

-4X^2-15X+604.3854459304

Back to the equation:

-(-4X^2-15X+604.3854459304)


We get rid of parentheses

4X^2+15X+X-604.3854459304=0

We add all the numbers together, and all the variables

4X^2+16X-604.3854459304=0

a = 4; b = 16; c = -604.3854459304;
Δ = b2-4ac
Δ = 162-4·4·(-604.3854459304)
Δ = 9926.1671348864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-\sqrt{9926.1671348864}}{2*4}=\frac{-16-\sqrt{9926.1671348864}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+\sqrt{9926.1671348864}}{2*4}=\frac{-16+\sqrt{9926.1671348864}}{8}
$