X+3=5/3x-1

Solution for X+3=5/3x-1 equation:

X+3=5/3X-1

We move all terms to the left:

X+3-(5/3X-1)=0


Domain of the equation: 3X-1)!=0

X∈R


We get rid of parentheses

X-5/3X+1+3=0

We multiply all the terms by the denominator


X*3X+1*3X+3*3X-5=0

Wy multiply elements

3X^2+3X+9X-5=0

We add all the numbers together, and all the variables

3X^2+12X-5=0

a = 3; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·3·(-5)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{51}}{2*3}=\frac{-12-2\sqrt{51}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{51}}{2*3}=\frac{-12+2\sqrt{51}}{6}
$