1/2x+10=352x

Solution for 1/2x+10=352x equation:

1/2x+10=352x

We move all terms to the left:

1/2x+10-(352x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-352x+1/2x+10=0

We multiply all the terms by the denominator


-352x*2x+10*2x+1=0

Wy multiply elements

-704x^2+20x+1=0

a = -704; b = 20; c = +1;
Δ = b2-4ac
Δ = 202-4·(-704)·1
Δ = 3216
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:

$\sqrt{\Delta}=\sqrt{3216}=\sqrt{16*201}=\sqrt{16}*\sqrt{201}=4\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{201}}{2*-704}=\frac{-20-4\sqrt{201}}{-1408}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{201}}{2*-704}=\frac{-20+4\sqrt{201}}{-1408}
$