10t^2+105t+30=75

Solution for 10t^2+105t+30=75 equation:

10t^2+105t+30=75

We move all terms to the left:

10t^2+105t+30-(75)=0

We add all the numbers together, and all the variables

10t^2+105t-45=0

a = 10; b = 105; c = -45;
Δ = b2-4ac
Δ = 1052-4·10·(-45)
Δ = 12825
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:

$\sqrt{\Delta}=\sqrt{12825}=\sqrt{225*57}=\sqrt{225}*\sqrt{57}=15\sqrt{57}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-15\sqrt{57}}{2*10}=\frac{-105-15\sqrt{57}}{20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+15\sqrt{57}}{2*10}=\frac{-105+15\sqrt{57}}{20}
$