1444=(76*x^2)/2

Solution for 1444=(76*x^2)/2 equation:

1444=(76x^2)/2

We move all terms to the left:

1444-((76x^2)/2)=0

We get rid of parentheses

-76x^2/2+1444=0

We multiply all the terms by the denominator


-76x^2+1444*2=0

We add all the numbers together, and all the variables

-76x^2+2888=0

a = -76; b = 0; c = +2888;
Δ = b2-4ac
Δ = 02-4·(-76)·2888
Δ = 877952
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:

$\sqrt{\Delta}=\sqrt{877952}=\sqrt{23104*38}=\sqrt{23104}*\sqrt{38}=152\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-152\sqrt{38}}{2*-76}=\frac{0-152\sqrt{38}}{-152}
=-\frac{152\sqrt{38}}{-152}
=-\frac{\sqrt{38}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+152\sqrt{38}}{2*-76}=\frac{0+152\sqrt{38}}{-152}
=\frac{152\sqrt{38}}{-152}
=\frac{\sqrt{38}}{-1}
$