R=8t^2+5t-6

Solution for R=8t^2+5t-6 equation:

=8R^2+5R-6

We move all terms to the left:

-(8R^2+5R-6)=0

We get rid of parentheses

-8R^2-5R+6=0

a = -8; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-8)·6
Δ = 217
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{-(-5)-\sqrt{217}}{2*-8}=\frac{5-\sqrt{217}}{-16}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*-8}=\frac{5+\sqrt{217}}{-16}
$