X=5/3y-10

Solution for X=5/3y-10 equation:

X=5/3X-10

We move all terms to the left:

X-(5/3X-10)=0


Domain of the equation: 3X-10)!=0

X∈R


We get rid of parentheses

X-5/3X+10=0

We multiply all the terms by the denominator


X*3X+10*3X-5=0

Wy multiply elements

3X^2+30X-5=0

a = 3; b = 30; c = -5;
Δ = b2-4ac
Δ = 302-4·3·(-5)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-8\sqrt{15}}{2*3}=\frac{-30-8\sqrt{15}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+8\sqrt{15}}{2*3}=\frac{-30+8\sqrt{15}}{6}
$