3x-6+8x+1/2x+4=80

Solution for 3x-6+8x+1/2x+4=80 equation:

3x-6+8x+1/2x+4=80

We move all terms to the left:

3x-6+8x+1/2x+4-(80)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

11x+1/2x-82=0

We multiply all the terms by the denominator


11x*2x-82*2x+1=0

Wy multiply elements

22x^2-164x+1=0

a = 22; b = -164; c = +1;
Δ = b2-4ac
Δ = -1642-4·22·1
Δ = 26808
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:

$\sqrt{\Delta}=\sqrt{26808}=\sqrt{4*6702}=\sqrt{4}*\sqrt{6702}=2\sqrt{6702}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-164)-2\sqrt{6702}}{2*22}=\frac{164-2\sqrt{6702}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-164)+2\sqrt{6702}}{2*22}=\frac{164+2\sqrt{6702}}{44}
$