X=2x(2x+5)+2(2x+5)(x+3)+2(x)(x+3)

Solution for X=2x(2x+5)+2(2x+5)(x+3)+2(x)(x+3) equation:

X=2X(2X+5)+2(2X+5)(X+3)+2(X)(X+3)

We move all terms to the left:

X-(2X(2X+5)+2(2X+5)(X+3)+2(X)(X+3))=0

We multiply parentheses ..

-(2X(2X+5)+2(+2X^2+6X+5X+15)+2X(X+3))+X=0


We calculate terms in parentheses: -(2X(2X+5)+2(+2X^2+6X+5X+15)+2X(X+3)), so:

2X(2X+5)+2(+2X^2+6X+5X+15)+2X(X+3)

determiningTheFunctionDomain
2(+2X^2+6X+5X+15)+2X(2X+5)+2X(X+3)

We multiply parentheses

4X^2+4X^2+2X^2+12X+10X+10X+6X+30

We add all the numbers together, and all the variables

10X^2+38X+30

Back to the equation:

-(10X^2+38X+30)


We add all the numbers together, and all the variables

X-(10X^2+38X+30)=0

We get rid of parentheses

-10X^2+X-38X-30=0

We add all the numbers together, and all the variables

-10X^2-37X-30=0

a = -10; b = -37; c = -30;
Δ = b2-4ac
Δ = -372-4·(-10)·(-30)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-13}{2*-10}=\frac{24}{-20}
=-1+1/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+13}{2*-10}=\frac{50}{-20}
=-2+1/2
$