3/4x+x=8

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

3/4x+x=8

We move all terms to the left:

3/4x+x-(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-8=0

We multiply all the terms by the denominator


x*4x-8*4x+3=0

Wy multiply elements

4x^2-32x+3=0

a = 4; b = -32; c = +3;
Δ = b2-4ac
Δ = -322-4·4·3
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{61}}{2*4}=\frac{32-4\sqrt{61}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{61}}{2*4}=\frac{32+4\sqrt{61}}{8}
$