82/7x-7x+2=17

Solution for 82/7x-7x+2=17 equation:

82/7x-7x+2=17

We move all terms to the left:

82/7x-7x+2-(17)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-7x+82/7x-15=0

We multiply all the terms by the denominator


-7x*7x-15*7x+82=0

Wy multiply elements

-49x^2-105x+82=0

a = -49; b = -105; c = +82;
Δ = b2-4ac
Δ = -1052-4·(-49)·82
Δ = 27097
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:

$\sqrt{\Delta}=\sqrt{27097}=\sqrt{49*553}=\sqrt{49}*\sqrt{553}=7\sqrt{553}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-7\sqrt{553}}{2*-49}=\frac{105-7\sqrt{553}}{-98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+7\sqrt{553}}{2*-49}=\frac{105+7\sqrt{553}}{-98}
$