4/5*x=810

Solution for 4/5*x=810 equation:

4/5*x=810

We move all terms to the left:

4/5*x-(810)=0


Domain of the equation: 5*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-810*5*x+4=0

Wy multiply elements

-4050x*x+4=0

Wy multiply elements

-4050x^2+4=0

a = -4050; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-4050)·4
Δ = 64800
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:

$\sqrt{\Delta}=\sqrt{64800}=\sqrt{32400*2}=\sqrt{32400}*\sqrt{2}=180\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-180\sqrt{2}}{2*-4050}=\frac{0-180\sqrt{2}}{-8100}
=-\frac{180\sqrt{2}}{-8100}
=-\frac{\sqrt{2}}{-45}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+180\sqrt{2}}{2*-4050}=\frac{0+180\sqrt{2}}{-8100}
=\frac{180\sqrt{2}}{-8100}
=\frac{\sqrt{2}}{-45}
$