Q(1/4)=6x^2-12

Solution for Q(1/4)=6x^2-12 equation:

(1/4)=6Q^2-12

We move all terms to the left:

(1/4)-(6Q^2-12)=0

We add all the numbers together, and all the variables

-(6Q^2-12)+(+1/4)=0

We get rid of parentheses

-6Q^2+12+1/4=0

We multiply all the terms by the denominator


-6Q^2*4+1+12*4=0

We add all the numbers together, and all the variables

-6Q^2*4+49=0

Wy multiply elements

-24Q^2+49=0

a = -24; b = 0; c = +49;
Δ = b2-4ac
Δ = 02-4·(-24)·49
Δ = 4704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4704}=\sqrt{784*6}=\sqrt{784}*\sqrt{6}=28\sqrt{6}$
$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{6}}{2*-24}=\frac{0-28\sqrt{6}}{-48}
=-\frac{28\sqrt{6}}{-48}
=-\frac{7\sqrt{6}}{-12}
$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{6}}{2*-24}=\frac{0+28\sqrt{6}}{-48}
=\frac{28\sqrt{6}}{-48}
=\frac{7\sqrt{6}}{-12}
$