X=(22+x)(154-6x)

Solution for X=(22+x)(154-6x) equation:

X=(22+X)(154-6X)

We move all terms to the left:

X-((22+X)(154-6X))=0

We add all the numbers together, and all the variables

X-((X+22)(-6X+154))=0

We multiply parentheses ..

-((-6X^2+154X-132X+3388))+X=0


We calculate terms in parentheses: -((-6X^2+154X-132X+3388)), so:

(-6X^2+154X-132X+3388)

We get rid of parentheses

-6X^2+154X-132X+3388

We add all the numbers together, and all the variables

-6X^2+22X+3388

Back to the equation:

-(-6X^2+22X+3388)


We get rid of parentheses

6X^2-22X+X-3388=0

We add all the numbers together, and all the variables

6X^2-21X-3388=0

a = 6; b = -21; c = -3388;
Δ = b2-4ac
Δ = -212-4·6·(-3388)
Δ = 81753
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{-(-21)-\sqrt{81753}}{2*6}=\frac{21-\sqrt{81753}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{81753}}{2*6}=\frac{21+\sqrt{81753}}{12}
$