X+1/2y=99

Solution for X+1/2y=99 equation:

X+1/2X=99

We move all terms to the left:

X+1/2X-(99)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-99*2X+1=0

Wy multiply elements

2X^2-198X+1=0

a = 2; b = -198; c = +1;
Δ = b2-4ac
Δ = -1982-4·2·1
Δ = 39196
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:

$\sqrt{\Delta}=\sqrt{39196}=\sqrt{4*9799}=\sqrt{4}*\sqrt{9799}=2\sqrt{9799}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-2\sqrt{9799}}{2*2}=\frac{198-2\sqrt{9799}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+2\sqrt{9799}}{2*2}=\frac{198+2\sqrt{9799}}{4}
$