18r^2-130r+28=0

Solution for 18r^2-130r+28=0 equation:

18r^2-130r+28=0

a = 18; b = -130; c = +28;
Δ = b2-4ac
Δ = -1302-4·18·28
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-122}{2*18}=\frac{8}{36}
=2/9
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+122}{2*18}=\frac{252}{36}
=7
$