X+5/2y=9

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

X+5/2X=9

We move all terms to the left:

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


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


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

Wy multiply elements

2X^2-18X+5=0

a = 2; b = -18; c = +5;
Δ = b2-4ac
Δ = -182-4·2·5
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{71}}{2*2}=\frac{18-2\sqrt{71}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{71}}{2*2}=\frac{18+2\sqrt{71}}{4}
$