X+4-3/4x=8

Solution for X+4-3/4x=8 equation:

X+4-3/4X=8

We move all terms to the left:

X+4-3/4X-(8)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We add all the numbers together, and all the variables

X-3/4X-4=0

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 = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{19}}{2*4}=\frac{16-4\sqrt{19}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{19}}{2*4}=\frac{16+4\sqrt{19}}{8}
$