45x^2=1600

Solution for 45x^2=1600 equation:

45x^2=1600

We move all terms to the left:

45x^2-(1600)=0

a = 45; b = 0; c = -1600;
Δ = b2-4ac
Δ = 02-4·45·(-1600)
Δ = 288000
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:

$\sqrt{\Delta}=\sqrt{288000}=\sqrt{57600*5}=\sqrt{57600}*\sqrt{5}=240\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-240\sqrt{5}}{2*45}=\frac{0-240\sqrt{5}}{90}
=-\frac{240\sqrt{5}}{90}
=-\frac{8\sqrt{5}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+240\sqrt{5}}{2*45}=\frac{0+240\sqrt{5}}{90}
=\frac{240\sqrt{5}}{90}
=\frac{8\sqrt{5}}{3}
$