3x*4x=678

Solution for 3x*4x=678 equation:

3x*4x=678

We move all terms to the left:

3x*4x-(678)=0

Wy multiply elements

12x^2-678=0

a = 12; b = 0; c = -678;
Δ = b2-4ac
Δ = 02-4·12·(-678)
Δ = 32544
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:

$\sqrt{\Delta}=\sqrt{32544}=\sqrt{144*226}=\sqrt{144}*\sqrt{226}=12\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{226}}{2*12}=\frac{0-12\sqrt{226}}{24}
=-\frac{12\sqrt{226}}{24}
=-\frac{\sqrt{226}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{226}}{2*12}=\frac{0+12\sqrt{226}}{24}
=\frac{12\sqrt{226}}{24}
=\frac{\sqrt{226}}{2}
$