X=9/2y-5

Solution for X=9/2y-5 equation:

X=9/2X-5

We move all terms to the left:

X-(9/2X-5)=0


Domain of the equation: 2X-5)!=0

X∈R


We get rid of parentheses

X-9/2X+5=0

We multiply all the terms by the denominator


X*2X+5*2X-9=0

Wy multiply elements

2X^2+10X-9=0

a = 2; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·2·(-9)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{43}}{2*2}=\frac{-10-2\sqrt{43}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{43}}{2*2}=\frac{-10+2\sqrt{43}}{4}
$