1/2x=92x+10

Solution for 1/2x=92x+10 equation:

1/2x=92x+10

We move all terms to the left:

1/2x-(92x+10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-92x-10=0

We multiply all the terms by the denominator


-92x*2x-10*2x+1=0

Wy multiply elements

-184x^2-20x+1=0

a = -184; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·(-184)·1
Δ = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{71}}{2*-184}=\frac{20-4\sqrt{71}}{-368}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{71}}{2*-184}=\frac{20+4\sqrt{71}}{-368}
$