X=7/6y-5

Solution for X=7/6y-5 equation:

X=7/6X-5

We move all terms to the left:

X-(7/6X-5)=0


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

X∈R


We get rid of parentheses

X-7/6X+5=0

We multiply all the terms by the denominator


X*6X+5*6X-7=0

Wy multiply elements

6X^2+30X-7=0

a = 6; b = 30; c = -7;
Δ = b2-4ac
Δ = 302-4·6·(-7)
Δ = 1068
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:

$\sqrt{\Delta}=\sqrt{1068}=\sqrt{4*267}=\sqrt{4}*\sqrt{267}=2\sqrt{267}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{267}}{2*6}=\frac{-30-2\sqrt{267}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{267}}{2*6}=\frac{-30+2\sqrt{267}}{12}
$