93=4x+1/2x

Solution for 93=4x+1/2x equation:

93=4x+1/2x

We move all terms to the left:

93-(4x+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+4x+1/2x)+93=0

We get rid of parentheses

-4x-1/2x+93=0

We multiply all the terms by the denominator


-4x*2x+93*2x-1=0

Wy multiply elements

-8x^2+186x-1=0

a = -8; b = 186; c = -1;
Δ = b2-4ac
Δ = 1862-4·(-8)·(-1)
Δ = 34564
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:

$\sqrt{\Delta}=\sqrt{34564}=\sqrt{4*8641}=\sqrt{4}*\sqrt{8641}=2\sqrt{8641}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(186)-2\sqrt{8641}}{2*-8}=\frac{-186-2\sqrt{8641}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(186)+2\sqrt{8641}}{2*-8}=\frac{-186+2\sqrt{8641}}{-16}
$