14x+6=17/17x+6=20

Solution for 14x+6=17/17x+6=20 equation:

14x+6=17/17x+6=20

We move all terms to the left:

14x+6-(17/17x+6)=0


Domain of the equation: 17x+6)!=0

x∈R


We get rid of parentheses

14x-17/17x-6+6=0

We multiply all the terms by the denominator


14x*17x-6*17x+6*17x-17=0

Wy multiply elements

238x^2-102x+102x-17=0

We add all the numbers together, and all the variables

238x^2-17=0

a = 238; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·238·(-17)
Δ = 16184
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:

$\sqrt{\Delta}=\sqrt{16184}=\sqrt{1156*14}=\sqrt{1156}*\sqrt{14}=34\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34\sqrt{14}}{2*238}=\frac{0-34\sqrt{14}}{476}
=-\frac{34\sqrt{14}}{476}
=-\frac{\sqrt{14}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34\sqrt{14}}{2*238}=\frac{0+34\sqrt{14}}{476}
=\frac{34\sqrt{14}}{476}
=\frac{\sqrt{14}}{14}
$