3/4x+6(x)=8

Solution for 3/4x+6(x)=8 equation:

3/4x+6(x)=8

We move all terms to the left:

3/4x+6(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

6x+3/4x-8=0

We multiply all the terms by the denominator


6x*4x-8*4x+3=0

Wy multiply elements

24x^2-32x+3=0

a = 24; b = -32; c = +3;
Δ = b2-4ac
Δ = -322-4·24·3
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{46}}{2*24}=\frac{32-4\sqrt{46}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{46}}{2*24}=\frac{32+4\sqrt{46}}{48}
$