5x+6-1/2x=3x-7

Solution for 5x+6-1/2x=3x-7 equation:

5x+6-1/2x=3x-7

We move all terms to the left:

5x+6-1/2x-(3x-7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5x-1/2x-3x+7+6=0

We multiply all the terms by the denominator


5x*2x-3x*2x+7*2x+6*2x-1=0

Wy multiply elements

10x^2-6x^2+14x+12x-1=0

We add all the numbers together, and all the variables

4x^2+26x-1=0

a = 4; b = 26; c = -1;
Δ = b2-4ac
Δ = 262-4·4·(-1)
Δ = 692
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:

$\sqrt{\Delta}=\sqrt{692}=\sqrt{4*173}=\sqrt{4}*\sqrt{173}=2\sqrt{173}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{173}}{2*4}=\frac{-26-2\sqrt{173}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{173}}{2*4}=\frac{-26+2\sqrt{173}}{8}
$