3x2-10/4=56

Solution for 3x2-10/4=56 equation:

3x^2-10/4=56

We move all terms to the left:

3x^2-10/4-(56)=0

determiningTheFunctionDomain
3x^2-56-10/4=0

We multiply all the terms by the denominator


3x^2*4-10-56*4=0

We add all the numbers together, and all the variables

3x^2*4-234=0

Wy multiply elements

12x^2-234=0

a = 12; b = 0; c = -234;
Δ = b2-4ac
Δ = 02-4·12·(-234)
Δ = 11232
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:

$\sqrt{\Delta}=\sqrt{11232}=\sqrt{144*78}=\sqrt{144}*\sqrt{78}=12\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{78}}{2*12}=\frac{0-12\sqrt{78}}{24}
=-\frac{12\sqrt{78}}{24}
=-\frac{\sqrt{78}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{78}}{2*12}=\frac{0+12\sqrt{78}}{24}
=\frac{12\sqrt{78}}{24}
=\frac{\sqrt{78}}{2}
$