-17/2x+7=x

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

-17/2x+7=x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-2x^2+14x-17=0

a = -2; b = 14; c = -17;
Δ = b2-4ac
Δ = 142-4·(-2)·(-17)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{15}}{2*-2}=\frac{-14-2\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{15}}{2*-2}=\frac{-14+2\sqrt{15}}{-4}
$