1/2x+17=7x

Solution for 1/2x+17=7x equation:

1/2x+17=7x

We move all terms to the left:

1/2x+17-(7x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-7x+1/2x+17=0

We multiply all the terms by the denominator


-7x*2x+17*2x+1=0

Wy multiply elements

-14x^2+34x+1=0

a = -14; b = 34; c = +1;
Δ = b2-4ac
Δ = 342-4·(-14)·1
Δ = 1212
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:

$\sqrt{\Delta}=\sqrt{1212}=\sqrt{4*303}=\sqrt{4}*\sqrt{303}=2\sqrt{303}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{303}}{2*-14}=\frac{-34-2\sqrt{303}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{303}}{2*-14}=\frac{-34+2\sqrt{303}}{-28}
$