0.5x*x=250/6

Solution for 0.5x*x=250/6 equation:

0.5x*x=250/6

We move all terms to the left:

0.5x*x-(250/6)=0

We add all the numbers together, and all the variables

0.5x*x-(+250/6)=0

We get rid of parentheses

0.5x*x-250/6=0

We multiply all the terms by the denominator


(0.5x*x)*6-250=0

We add all the numbers together, and all the variables

(+0.5x*x)*6-250=0

We multiply parentheses

0x^2-250=0

We add all the numbers together, and all the variables

x^2-250=0

a = 1; b = 0; c = -250;
Δ = b2-4ac
Δ = 02-4·1·(-250)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{10}}{2*1}=\frac{0-10\sqrt{10}}{2}
=-\frac{10\sqrt{10}}{2}
=-5\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{10}}{2*1}=\frac{0+10\sqrt{10}}{2}
=\frac{10\sqrt{10}}{2}
=5\sqrt{10}
$