1/2(6x^2)=115

Solution for 1/2(6x^2)=115 equation:

1/2(6x^2)=115

We move all terms to the left:

1/2(6x^2)-(115)=0


Domain of the equation: 26x^2!=0

x^2!=0/26

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-115*26x^2+1=0

Wy multiply elements

-2990x^2+1=0

a = -2990; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-2990)·1
Δ = 11960
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:

$\sqrt{\Delta}=\sqrt{11960}=\sqrt{4*2990}=\sqrt{4}*\sqrt{2990}=2\sqrt{2990}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2990}}{2*-2990}=\frac{0-2\sqrt{2990}}{-5980}
=-\frac{2\sqrt{2990}}{-5980}
=-\frac{\sqrt{2990}}{-2990}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2990}}{2*-2990}=\frac{0+2\sqrt{2990}}{-5980}
=\frac{2\sqrt{2990}}{-5980}
=\frac{\sqrt{2990}}{-2990}
$