R=2t^2+87t+90

Solution for R=2t^2+87t+90 equation:

=2R^2+87R+90

We move all terms to the left:

-(2R^2+87R+90)=0

We get rid of parentheses

-2R^2-87R-90=0

a = -2; b = -87; c = -90;
Δ = b2-4ac
Δ = -872-4·(-2)·(-90)
Δ = 6849
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:

$\sqrt{\Delta}=\sqrt{6849}=\sqrt{9*761}=\sqrt{9}*\sqrt{761}=3\sqrt{761}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-87)-3\sqrt{761}}{2*-2}=\frac{87-3\sqrt{761}}{-4}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+3\sqrt{761}}{2*-2}=\frac{87+3\sqrt{761}}{-4}
$