X=1/3y+20

Solution for X=1/3y+20 equation:

X=1/3X+20

We move all terms to the left:

X-(1/3X+20)=0


Domain of the equation: 3X+20)!=0

X∈R


We get rid of parentheses

X-1/3X-20=0

We multiply all the terms by the denominator


X*3X-20*3X-1=0

Wy multiply elements

3X^2-60X-1=0

a = 3; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·3·(-1)
Δ = 3612
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:

$\sqrt{\Delta}=\sqrt{3612}=\sqrt{4*903}=\sqrt{4}*\sqrt{903}=2\sqrt{903}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{903}}{2*3}=\frac{60-2\sqrt{903}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{903}}{2*3}=\frac{60+2\sqrt{903}}{6}
$