7+24/6x2=13

Solution for 7+24/6x2=13 equation:

7+24/6x^2=13

We move all terms to the left:

7+24/6x^2-(13)=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

24/6x^2-6=0

We multiply all the terms by the denominator


-6*6x^2+24=0

Wy multiply elements

-36x^2+24=0

a = -36; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-36)·24
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{6}}{2*-36}=\frac{0-24\sqrt{6}}{-72}
=-\frac{24\sqrt{6}}{-72}
=-\frac{\sqrt{6}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{6}}{2*-36}=\frac{0+24\sqrt{6}}{-72}
=\frac{24\sqrt{6}}{-72}
=\frac{\sqrt{6}}{-3}
$