3(3.4)=-5t^2+14t+3

Solution for 3(3.4)=-5t^2+14t+3 equation:

3(3.4)=-5t^2+14t+3

We move all terms to the left:

3(3.4)-(-5t^2+14t+3)=0

We add all the numbers together, and all the variables

-(-5t^2+14t+3)+10.2=0

We get rid of parentheses

5t^2-14t-3+10.2=0

We add all the numbers together, and all the variables

5t^2-14t+7.2=0

a = 5; b = -14; c = +7.2;
Δ = b2-4ac
Δ = -142-4·5·7.2
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{13}}{2*5}=\frac{14-2\sqrt{13}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{13}}{2*5}=\frac{14+2\sqrt{13}}{10}
$