206=(6x+22)(x+37)

Solution for 206=(6x+22)(x+37) equation:

206=(6x+22)(x+37)

We move all terms to the left:

206-((6x+22)(x+37))=0

We multiply parentheses ..

-((+6x^2+222x+22x+814))+206=0


We calculate terms in parentheses: -((+6x^2+222x+22x+814)), so:

(+6x^2+222x+22x+814)

We get rid of parentheses

6x^2+222x+22x+814

We add all the numbers together, and all the variables

6x^2+244x+814

Back to the equation:

-(6x^2+244x+814)


We get rid of parentheses

-6x^2-244x-814+206=0

We add all the numbers together, and all the variables

-6x^2-244x-608=0

a = -6; b = -244; c = -608;
Δ = b2-4ac
Δ = -2442-4·(-6)·(-608)
Δ = 44944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{44944}=212$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-244)-212}{2*-6}=\frac{32}{-12}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-244)+212}{2*-6}=\frac{456}{-12}
=-38
$