195/360*r+r=10.25

Solution for 195/360*r+r=10.25 equation:

195/360r+r=10.25

We move all terms to the left:

195/360r+r-(10.25)=0


Domain of the equation: 360r!=0

r!=0/360

r!=0

r∈R


We add all the numbers together, and all the variables

r+195/360r-10.25=0

We multiply all the terms by the denominator


r*360r-(10.25)*360r+195=0

We multiply parentheses

r*360r-3690r+195=0

Wy multiply elements

360r^2-3690r+195=0

a = 360; b = -3690; c = +195;
Δ = b2-4ac
Δ = -36902-4·360·195
Δ = 13335300
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:

$\sqrt{\Delta}=\sqrt{13335300}=\sqrt{900*14817}=\sqrt{900}*\sqrt{14817}=30\sqrt{14817}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3690)-30\sqrt{14817}}{2*360}=\frac{3690-30\sqrt{14817}}{720}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3690)+30\sqrt{14817}}{2*360}=\frac{3690+30\sqrt{14817}}{720}
$