242=(x/2)(11+3x)

Solution for 242=(x/2)(11+3x) equation:

242=(x/2)(11+3x)

We move all terms to the left:

242-((x/2)(11+3x))=0


Domain of the equation: 2)(11+3x))!=0

x∈R


We add all the numbers together, and all the variables

-((+x/2)(3x+11))+242=0

We multiply parentheses ..

-((+3x^2+11x))+242=0


We calculate terms in parentheses: -((+3x^2+11x)), so:

(+3x^2+11x)

We get rid of parentheses

3x^2+11x

Back to the equation:

-(3x^2+11x)


We get rid of parentheses

-3x^2-11x+242=0

a = -3; b = -11; c = +242;
Δ = b2-4ac
Δ = -112-4·(-3)·242
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-55}{2*-3}=\frac{-44}{-6}
=7+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+55}{2*-3}=\frac{66}{-6}
=-11
$