x+5x+1/2x+2x=9.50

Solution for x+5x+1/2x+2x=9.50 equation:

x+5x+1/2x+2x=9.50

We move all terms to the left:

x+5x+1/2x+2x-(9.50)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+5x+1/2x+2x-(9.5)=0

We add all the numbers together, and all the variables

8x+1/2x-9.5=0

We multiply all the terms by the denominator


8x*2x-(9.5)*2x+1=0

We multiply parentheses

8x*2x-19x+1=0

Wy multiply elements

16x^2-19x+1=0

a = 16; b = -19; c = +1;
Δ = b2-4ac
Δ = -192-4·16·1
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{33}}{2*16}=\frac{19-3\sqrt{33}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{33}}{2*16}=\frac{19+3\sqrt{33}}{32}
$