0.5(5)x^2=1000

Solution for 0.5(5)x^2=1000 equation:

0.5(5)x^2=1000

We move all terms to the left:

0.5(5)x^2-(1000)=0

a = 0.55; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·0.55·(-1000)
Δ = 2200
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:

$\sqrt{\Delta}=\sqrt{2200}=\sqrt{100*22}=\sqrt{100}*\sqrt{22}=10\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{22}}{2*0.55}=\frac{0-10\sqrt{22}}{1.1}
=-\frac{10\sqrt{22}}{1.1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{22}}{2*0.55}=\frac{0+10\sqrt{22}}{1.1}
=\frac{10\sqrt{22}}{1.1}
$