38+x=(3x+2)x

Solution for 38+x=(3x+2)x equation:

38+x=(3x+2)x

We move all terms to the left:

38+x-((3x+2)x)=0


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

(3x+2)x

We multiply parentheses

3x^2+2x

Back to the equation:

-(3x^2+2x)


We get rid of parentheses

-3x^2+x-2x+38=0

We add all the numbers together, and all the variables

-3x^2-1x+38=0

a = -3; b = -1; c = +38;
Δ = b2-4ac
Δ = -12-4·(-3)·38
Δ = 457
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{-(-1)-\sqrt{457}}{2*-3}=\frac{1-\sqrt{457}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{457}}{2*-3}=\frac{1+\sqrt{457}}{-6}
$