6x^2=25/4

Solution for 6x^2=25/4 equation:

6x^2=25/4

We move all terms to the left:

6x^2-(25/4)=0

We add all the numbers together, and all the variables

6x^2-(+25/4)=0

We get rid of parentheses

6x^2-25/4=0

We multiply all the terms by the denominator


6x^2*4-25=0

Wy multiply elements

24x^2-25=0

a = 24; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·24·(-25)
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*24}=\frac{0-20\sqrt{6}}{48}
=-\frac{20\sqrt{6}}{48}
=-\frac{5\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*24}=\frac{0+20\sqrt{6}}{48}
=\frac{20\sqrt{6}}{48}
=\frac{5\sqrt{6}}{12}
$