3x*2x-5=684

Solution for 3x*2x-5=684 equation:

3x*2x-5=684

We move all terms to the left:

3x*2x-5-(684)=0

We add all the numbers together, and all the variables

3x*2x-689=0

Wy multiply elements

6x^2-689=0

a = 6; b = 0; c = -689;
Δ = b2-4ac
Δ = 02-4·6·(-689)
Δ = 16536
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:

$\sqrt{\Delta}=\sqrt{16536}=\sqrt{4*4134}=\sqrt{4}*\sqrt{4134}=2\sqrt{4134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{4134}}{2*6}=\frac{0-2\sqrt{4134}}{12}
=-\frac{2\sqrt{4134}}{12}
=-\frac{\sqrt{4134}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{4134}}{2*6}=\frac{0+2\sqrt{4134}}{12}
=\frac{2\sqrt{4134}}{12}
=\frac{\sqrt{4134}}{6}
$