5x-1/2x+3=6

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

5x-1/2x+3=6

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5x-1/2x-3=0

We multiply all the terms by the denominator


5x*2x-3*2x-1=0

Wy multiply elements

10x^2-6x-1=0

a = 10; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·10·(-1)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*10}=\frac{6-2\sqrt{19}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*10}=\frac{6+2\sqrt{19}}{20}
$