6x(1/4)=38

Solution for 6x(1/4)=38 equation:

6x(1/4)=38

We move all terms to the left:

6x(1/4)-(38)=0

We add all the numbers together, and all the variables

6x(+1/4)-38=0

We multiply parentheses

6x^2-38=0

a = 6; b = 0; c = -38;
Δ = b2-4ac
Δ = 02-4·6·(-38)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{57}}{2*6}=\frac{0-4\sqrt{57}}{12}
=-\frac{4\sqrt{57}}{12}
=-\frac{\sqrt{57}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{57}}{2*6}=\frac{0+4\sqrt{57}}{12}
=\frac{4\sqrt{57}}{12}
=\frac{\sqrt{57}}{3}
$