(41/2)x=510000

Solution for (41/2)x=510000 equation:

(41/2)x=510000

We move all terms to the left:

(41/2)x-(510000)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+41/2)x-510000=0

We multiply parentheses

41x^2-510000=0

a = 41; b = 0; c = -510000;
Δ = b2-4ac
Δ = 02-4·41·(-510000)
Δ = 83640000
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:

$\sqrt{\Delta}=\sqrt{83640000}=\sqrt{40000*2091}=\sqrt{40000}*\sqrt{2091}=200\sqrt{2091}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{2091}}{2*41}=\frac{0-200\sqrt{2091}}{82}
=-\frac{200\sqrt{2091}}{82}
=-\frac{100\sqrt{2091}}{41}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{2091}}{2*41}=\frac{0+200\sqrt{2091}}{82}
=\frac{200\sqrt{2091}}{82}
=\frac{100\sqrt{2091}}{41}
$