2x-92.75+31/4x=-42

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Solution for 2x-92.75+31/4x=-42 equation: 



2x-92.75+31/4x=-42

We move all terms to the left:

2x-92.75+31/4x-(-42)=0



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



We add all the numbers together, and all the variables

2x+31/4x-50.75=0

We multiply all the terms by the denominator


2x*4x-(50.75)*4x+31=0

We multiply parentheses

2x*4x-203x+31=0

Wy multiply elements

8x^2-203x+31=0

a = 8; b = -203; c = +31;
Δ = b2-4ac
Δ = -2032-4·8·31
Δ = 40217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-203)-\sqrt{40217}}{2*8}=\frac{203-\sqrt{40217}}{16}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-203)+\sqrt{40217}}{2*8}=\frac{203+\sqrt{40217}}{16}
$

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