22t=-6t^2+42t+3.75

Solution for 22t=-6t^2+42t+3.75 equation:

22t=-6t^2+42t+3.75

We move all terms to the left:

22t-(-6t^2+42t+3.75)=0

We get rid of parentheses

6t^2-42t+22t-3.75=0

We add all the numbers together, and all the variables

6t^2-20t-3.75=0

a = 6; b = -20; c = -3.75;
Δ = b2-4ac
Δ = -202-4·6·(-3.75)
Δ = 490
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:

$\sqrt{\Delta}=\sqrt{490}=\sqrt{49*10}=\sqrt{49}*\sqrt{10}=7\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-7\sqrt{10}}{2*6}=\frac{20-7\sqrt{10}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+7\sqrt{10}}{2*6}=\frac{20+7\sqrt{10}}{12}
$