2(1/4)r=10

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Solution for 2(1/4)r=10 equation:



2(1/4)r=10
We move all terms to the left:
2(1/4)r-(10)=0
Domain of the equation: 4)r!=0
r!=0/1
r!=0
r∈R
We add all the numbers together, and all the variables
2(+1/4)r-10=0
We multiply parentheses
2r^2-10=0
a = 2; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·2·(-10)
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*2}=\frac{0-4\sqrt{5}}{4} =-\frac{4\sqrt{5}}{4} =-\sqrt{5} $
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*2}=\frac{0+4\sqrt{5}}{4} =\frac{4\sqrt{5}}{4} =\sqrt{5} $

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