3t+14=2t2-3t

Solution for 3t+14=2t2-3t equation:

3t+14=2t^2-3t

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2t^2+6t+14=0

a = -2; b = 6; c = +14;
Δ = b2-4ac
Δ = 62-4·(-2)·14
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{37}}{2*-2}=\frac{-6-2\sqrt{37}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{37}}{2*-2}=\frac{-6+2\sqrt{37}}{-4}
$