X=-6+5/2y

Solution for X=-6+5/2y equation:

X=-6+5/2X

We move all terms to the left:

X-(-6+5/2X)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(5/2X-6)=0

We get rid of parentheses

X-5/2X+6=0

We multiply all the terms by the denominator


X*2X+6*2X-5=0

Wy multiply elements

2X^2+12X-5=0

a = 2; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·2·(-5)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{46}}{2*2}=\frac{-12-2\sqrt{46}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{46}}{2*2}=\frac{-12+2\sqrt{46}}{4}
$