X+3/4x=100

Solution for X+3/4x=100 equation:

X+3/4X=100

We move all terms to the left:

X+3/4X-(100)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-100*4X+3=0

Wy multiply elements

4X^2-400X+3=0

a = 4; b = -400; c = +3;
Δ = b2-4ac
Δ = -4002-4·4·3
Δ = 159952
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:

$\sqrt{\Delta}=\sqrt{159952}=\sqrt{16*9997}=\sqrt{16}*\sqrt{9997}=4\sqrt{9997}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-4\sqrt{9997}}{2*4}=\frac{400-4\sqrt{9997}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+4\sqrt{9997}}{2*4}=\frac{400+4\sqrt{9997}}{8}
$