109=x(3x+17)

Solution for 109=x(3x+17) equation:

109=x(3x+17)

We move all terms to the left:

109-(x(3x+17))=0


We calculate terms in parentheses: -(x(3x+17)), so:

x(3x+17)

We multiply parentheses

3x^2+17x

Back to the equation:

-(3x^2+17x)


We get rid of parentheses

-3x^2-17x+109=0

a = -3; b = -17; c = +109;
Δ = b2-4ac
Δ = -172-4·(-3)·109
Δ = 1597
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{-(-17)-\sqrt{1597}}{2*-3}=\frac{17-\sqrt{1597}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{1597}}{2*-3}=\frac{17+\sqrt{1597}}{-6}
$