X(3x+17)=109

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

X(3X+17)=109

We move all terms to the left:

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

We multiply 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}
$