5/2x+0.5x=14+7/2x

Solution for 5/2x+0.5x=14+7/2x equation:

5/2x+0.5x=14+7/2x

We move all terms to the left:

5/2x+0.5x-(14+7/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x+0.5x-(7/2x+14)=0

We add all the numbers together, and all the variables

0.5x+5/2x-(7/2x+14)=0

We get rid of parentheses

0.5x+5/2x-7/2x-14=0

We multiply all the terms by the denominator


(0.5x)*2x-14*2x+5-7=0

We add all the numbers together, and all the variables

(+0.5x)*2x-14*2x+5-7=0

We add all the numbers together, and all the variables

(+0.5x)*2x-14*2x-2=0

We multiply parentheses

0x^2-14*2x-2=0

Wy multiply elements

0x^2-28x-2=0

We add all the numbers together, and all the variables

x^2-28x-2=0

a = 1; b = -28; c = -2;
Δ = b2-4ac
Δ = -282-4·1·(-2)
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-6\sqrt{22}}{2*1}=\frac{28-6\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+6\sqrt{22}}{2*1}=\frac{28+6\sqrt{22}}{2}
$