1/5x+6=115x-6=95x+6=216x+5=17

Solution for 1/5x+6=115x-6=95x+6=216x+5=17 equation:

1/5x+6=115x-6=95x+6=216x+5=17

We move all terms to the left:

1/5x+6-(115x-6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-115x+6+6=0

We multiply all the terms by the denominator


-115x*5x+6*5x+6*5x+1=0

Wy multiply elements

-575x^2+30x+30x+1=0

We add all the numbers together, and all the variables

-575x^2+60x+1=0

a = -575; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·(-575)·1
Δ = 5900
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:

$\sqrt{\Delta}=\sqrt{5900}=\sqrt{100*59}=\sqrt{100}*\sqrt{59}=10\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-10\sqrt{59}}{2*-575}=\frac{-60-10\sqrt{59}}{-1150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+10\sqrt{59}}{2*-575}=\frac{-60+10\sqrt{59}}{-1150}
$