3x-17/2x+8=1

Solution for 3x-17/2x+8=1 equation:

3x-17/2x+8=1

We move all terms to the left:

3x-17/2x+8-(1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x-17/2x+7=0

We multiply all the terms by the denominator


3x*2x+7*2x-17=0

Wy multiply elements

6x^2+14x-17=0

a = 6; b = 14; c = -17;
Δ = b2-4ac
Δ = 142-4·6·(-17)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{151}}{2*6}=\frac{-14-2\sqrt{151}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{151}}{2*6}=\frac{-14+2\sqrt{151}}{12}
$