35r^2=-17r-2

Solution for 35r^2=-17r-2 equation:

35r^2=-17r-2

We move all terms to the left:

35r^2-(-17r-2)=0

We get rid of parentheses

35r^2+17r+2=0

a = 35; b = 17; c = +2;
Δ = b2-4ac
Δ = 172-4·35·2
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{-(17)-3}{2*35}=\frac{-20}{70}
=-2/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3}{2*35}=\frac{-14}{70}
=-1/5
$