21/4*r=10

Solution for 21/4*r=10 equation:

21/4*r=10

We move all terms to the left:

21/4*r-(10)=0


Domain of the equation: 4*r!=0

r!=0/1

r!=0

r∈R


We multiply all the terms by the denominator


-10*4*r+21=0

Wy multiply elements

-40r*r+21=0

Wy multiply elements

-40r^2+21=0

a = -40; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-40)·21
Δ = 3360
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:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{210}}{2*-40}=\frac{0-4\sqrt{210}}{-80}
=-\frac{4\sqrt{210}}{-80}
=-\frac{\sqrt{210}}{-20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{210}}{2*-40}=\frac{0+4\sqrt{210}}{-80}
=\frac{4\sqrt{210}}{-80}
=\frac{\sqrt{210}}{-20}
$