X+41/2y=100

Solution for X+41/2y=100 equation:

X+41/2X=100

We move all terms to the left:

X+41/2X-(100)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-100*2X+41=0

Wy multiply elements

2X^2-200X+41=0

a = 2; b = -200; c = +41;
Δ = b2-4ac
Δ = -2002-4·2·41
Δ = 39672
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:

$\sqrt{\Delta}=\sqrt{39672}=\sqrt{36*1102}=\sqrt{36}*\sqrt{1102}=6\sqrt{1102}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-6\sqrt{1102}}{2*2}=\frac{200-6\sqrt{1102}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+6\sqrt{1102}}{2*2}=\frac{200+6\sqrt{1102}}{4}
$