X+3/4x=63

Solution for X+3/4x=63 equation:

X+3/4X=63

We move all terms to the left:

X+3/4X-(63)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-63*4X+3=0

Wy multiply elements

4X^2-252X+3=0

a = 4; b = -252; c = +3;
Δ = b2-4ac
Δ = -2522-4·4·3
Δ = 63456
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:

$\sqrt{\Delta}=\sqrt{63456}=\sqrt{16*3966}=\sqrt{16}*\sqrt{3966}=4\sqrt{3966}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-4\sqrt{3966}}{2*4}=\frac{252-4\sqrt{3966}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+4\sqrt{3966}}{2*4}=\frac{252+4\sqrt{3966}}{8}
$