X=5/2y-3

Solution for X=5/2y-3 equation:

X=5/2X-3

We move all terms to the left:

X-(5/2X-3)=0


Domain of the equation: 2X-3)!=0

X∈R


We get rid of parentheses

X-5/2X+3=0

We multiply all the terms by the denominator


X*2X+3*2X-5=0

Wy multiply elements

2X^2+6X-5=0

a = 2; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·2·(-5)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{19}}{2*2}=\frac{-6-2\sqrt{19}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{19}}{2*2}=\frac{-6+2\sqrt{19}}{4}
$