5r^2-3+r=28

Solution for 5r^2-3+r=28 equation:

5r^2-3+r=28

We move all terms to the left:

5r^2-3+r-(28)=0

We add all the numbers together, and all the variables

5r^2+r-31=0

a = 5; b = 1; c = -31;
Δ = b2-4ac
Δ = 12-4·5·(-31)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{69}}{2*5}=\frac{-1-3\sqrt{69}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{69}}{2*5}=\frac{-1+3\sqrt{69}}{10}
$