7x-2=9x+5-1/2x

Solution for 7x-2=9x+5-1/2x equation:

7x-2=9x+5-1/2x

We move all terms to the left:

7x-2-(9x+5-1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-(9x-1/2x+5)-2=0

We get rid of parentheses

7x-9x+1/2x-5-2=0

We multiply all the terms by the denominator


7x*2x-9x*2x-5*2x-2*2x+1=0

Wy multiply elements

14x^2-18x^2-10x-4x+1=0

We add all the numbers together, and all the variables

-4x^2-14x+1=0

a = -4; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·(-4)·1
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{53}}{2*-4}=\frac{14-2\sqrt{53}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{53}}{2*-4}=\frac{14+2\sqrt{53}}{-8}
$