X-6/3x+2=-3

Solution for X-6/3x+2=-3 equation:

X-6/3X+2=-3

We move all terms to the left:

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


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X-6/3X+5=0

We multiply all the terms by the denominator


X*3X+5*3X-6=0

Wy multiply elements

3X^2+15X-6=0

a = 3; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·3·(-6)
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{33}}{2*3}=\frac{-15-3\sqrt{33}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{33}}{2*3}=\frac{-15+3\sqrt{33}}{6}
$