5t+10t^2=45

Solution for 5t+10t^2=45 equation:

5t+10t^2=45

We move all terms to the left:

5t+10t^2-(45)=0

a = 10; b = 5; c = -45;
Δ = b2-4ac
Δ = 52-4·10·(-45)
Δ = 1825
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{73}}{2*10}=\frac{-5-5\sqrt{73}}{20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{73}}{2*10}=\frac{-5+5\sqrt{73}}{20}
$