194=1/2x+2x-8

Solution for 194=1/2x+2x-8 equation:

194=1/2x+2x-8

We move all terms to the left:

194-(1/2x+2x-8)=0


Domain of the equation: 2x+2x-8)!=0

x∈R


We add all the numbers together, and all the variables

-(2x+1/2x-8)+194=0

We get rid of parentheses

-2x-1/2x+8+194=0

We multiply all the terms by the denominator


-2x*2x+8*2x+194*2x-1=0

Wy multiply elements

-4x^2+16x+388x-1=0

We add all the numbers together, and all the variables

-4x^2+404x-1=0

a = -4; b = 404; c = -1;
Δ = b2-4ac
Δ = 4042-4·(-4)·(-1)
Δ = 163200
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:

$\sqrt{\Delta}=\sqrt{163200}=\sqrt{1600*102}=\sqrt{1600}*\sqrt{102}=40\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(404)-40\sqrt{102}}{2*-4}=\frac{-404-40\sqrt{102}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(404)+40\sqrt{102}}{2*-4}=\frac{-404+40\sqrt{102}}{-8}
$