10r^2=27r-18

Solution for 10r^2=27r-18 equation:

10r^2=27r-18

We move all terms to the left:

10r^2-(27r-18)=0

We get rid of parentheses

10r^2-27r+18=0

a = 10; b = -27; c = +18;
Δ = b2-4ac
Δ = -272-4·10·18
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3}{2*10}=\frac{24}{20}
=1+1/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3}{2*10}=\frac{30}{20}
=1+1/2
$