4/6x^2+10=34

Solution for 4/6x^2+10=34 equation:

4/6x^2+10=34

We move all terms to the left:

4/6x^2+10-(34)=0


Domain of the equation: 6x^2!=0

x^2!=0/6

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

4/6x^2-24=0

We multiply all the terms by the denominator


-24*6x^2+4=0

Wy multiply elements

-144x^2+4=0

a = -144; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-144)·4
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*-144}=\frac{-48}{-288}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*-144}=\frac{48}{-288}
=-1/6
$