1/2x-5x+6=0

Solution for 1/2x-5x+6=0 equation:

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -10; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-10)·1
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{46}}{2*-10}=\frac{-12-2\sqrt{46}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{46}}{2*-10}=\frac{-12+2\sqrt{46}}{-20}
$