X=5/3y+1

Solution for X=5/3y+1 equation:

X=5/3X+1

We move all terms to the left:

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


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

X∈R


We get rid of parentheses

X-5/3X-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

3X^2-3X-5=0

a = 3; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·3·(-5)
Δ = 69
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{-(-3)-\sqrt{69}}{2*3}=\frac{3-\sqrt{69}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{69}}{2*3}=\frac{3+\sqrt{69}}{6}
$