17-3(2x-7)=7x-3)2x-1)

Solution for 17-3(2x-7)=7x-3)2x-1) equation:

17-3(2x-7)=7x-3)2x-1)

We move all terms to the left:

17-3(2x-7)-(7x-3)2x-1))=0

We add all the numbers together, and all the variables

-3(2x-7)-(7x-3)2x=0

We multiply parentheses

-14x^2-6x+6x+21=0

We add all the numbers together, and all the variables

-14x^2+21=0

a = -14; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-14)·21
Δ = 1176
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:

$\sqrt{\Delta}=\sqrt{1176}=\sqrt{196*6}=\sqrt{196}*\sqrt{6}=14\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{6}}{2*-14}=\frac{0-14\sqrt{6}}{-28}
=-\frac{14\sqrt{6}}{-28}
=-\frac{\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{6}}{2*-14}=\frac{0+14\sqrt{6}}{-28}
=\frac{14\sqrt{6}}{-28}
=\frac{\sqrt{6}}{-2}
$