5r^2+3r=1

Solution for 5r^2+3r=1 equation:

5r^2+3r=1

We move all terms to the left:

5r^2+3r-(1)=0

a = 5; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·5·(-1)
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{29}}{2*5}=\frac{-3-\sqrt{29}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{29}}{2*5}=\frac{-3+\sqrt{29}}{10}
$