38=x(3x+7)

Solution for 38=x(3x+7) equation:

38=x(3x+7)

We move all terms to the left:

38-(x(3x+7))=0


We calculate terms in parentheses: -(x(3x+7)), so:

x(3x+7)

We multiply parentheses

3x^2+7x

Back to the equation:

-(3x^2+7x)


We get rid of parentheses

-3x^2-7x+38=0

a = -3; b = -7; c = +38;
Δ = b2-4ac
Δ = -72-4·(-3)·38
Δ = 505
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{-(-7)-\sqrt{505}}{2*-3}=\frac{7-\sqrt{505}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{505}}{2*-3}=\frac{7+\sqrt{505}}{-6}
$