X+3/4x=50

Solution for X+3/4x=50 equation:

X+3/4X=50

We move all terms to the left:

X+3/4X-(50)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-50*4X+3=0

Wy multiply elements

4X^2-200X+3=0

a = 4; b = -200; c = +3;
Δ = b2-4ac
Δ = -2002-4·4·3
Δ = 39952
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:

$\sqrt{\Delta}=\sqrt{39952}=\sqrt{16*2497}=\sqrt{16}*\sqrt{2497}=4\sqrt{2497}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-4\sqrt{2497}}{2*4}=\frac{200-4\sqrt{2497}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+4\sqrt{2497}}{2*4}=\frac{200+4\sqrt{2497}}{8}
$