X+3/4y=4

Solution for X+3/4y=4 equation:

X+3/4X=4

We move all terms to the left:

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


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


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

Wy multiply elements

4X^2-16X+3=0

a = 4; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·4·3
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{13}}{2*4}=\frac{16-4\sqrt{13}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{13}}{2*4}=\frac{16+4\sqrt{13}}{8}
$