27000=1/2(900)(x)^2

Solution for 27000=1/2(900)(x)^2 equation:

27000=1/2(900)(x)^2

We move all terms to the left:

27000-(1/2(900)(x)^2)=0


Domain of the equation: 2900x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/2900x^2+27000=0

We multiply all the terms by the denominator


27000*2900x^2-1=0

Wy multiply elements

78300000x^2-1=0

a = 78300000; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·78300000·(-1)
Δ = 313200000
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:

$\sqrt{\Delta}=\sqrt{313200000}=\sqrt{360000*870}=\sqrt{360000}*\sqrt{870}=600\sqrt{870}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-600\sqrt{870}}{2*78300000}=\frac{0-600\sqrt{870}}{156600000}
=-\frac{600\sqrt{870}}{156600000}
=-\frac{\sqrt{870}}{261000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+600\sqrt{870}}{2*78300000}=\frac{0+600\sqrt{870}}{156600000}
=\frac{600\sqrt{870}}{156600000}
=\frac{\sqrt{870}}{261000}
$