X=3/5y-6

Solution for X=3/5y-6 equation:

X=3/5X-6

We move all terms to the left:

X-(3/5X-6)=0


Domain of the equation: 5X-6)!=0

X∈R


We get rid of parentheses

X-3/5X+6=0

We multiply all the terms by the denominator


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

Wy multiply elements

5X^2+30X-3=0

a = 5; b = 30; c = -3;
Δ = b2-4ac
Δ = 302-4·5·(-3)
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*5}=\frac{-30-8\sqrt{15}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+8\sqrt{15}}{2*5}=\frac{-30+8\sqrt{15}}{10}
$