6X(2X+3)=x

Solution for 6X(2X+3)=x equation:

6X(2X+3)=X

We move all terms to the left:

6X(2X+3)-(X)=0

We add all the numbers together, and all the variables

-1X+6X(2X+3)=0

We multiply parentheses

12X^2-1X+18X=0

We add all the numbers together, and all the variables

12X^2+17X=0

a = 12; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·12·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*12}=\frac{-34}{24}
=-1+5/12
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*12}=\frac{0}{24}
=0
$