5-x=7/2x

Solution for 5-x=7/2x equation:

5-x=7/2x

We move all terms to the left:

5-x-(7/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x-(+7/2x)+5=0

We get rid of parentheses

-1x-7/2x+5=0

We multiply all the terms by the denominator


-1x*2x+5*2x-7=0

Wy multiply elements

-2x^2+10x-7=0

a = -2; b = 10; c = -7;
Δ = b2-4ac
Δ = 102-4·(-2)·(-7)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{11}}{2*-2}=\frac{-10-2\sqrt{11}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{11}}{2*-2}=\frac{-10+2\sqrt{11}}{-4}
$