5t2+12t-45=0

Solution for 5t2+12t-45=0 equation:

5t^2+12t-45=0

a = 5; b = 12; c = -45;
Δ = b2-4ac
Δ = 122-4·5·(-45)
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{29}}{2*5}=\frac{-12-6\sqrt{29}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{29}}{2*5}=\frac{-12+6\sqrt{29}}{10}
$