3t^2=974

Solution for 3t^2=974 equation:

3t^2=974

We move all terms to the left:

3t^2-(974)=0

a = 3; b = 0; c = -974;
Δ = b2-4ac
Δ = 02-4·3·(-974)
Δ = 11688
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:

$\sqrt{\Delta}=\sqrt{11688}=\sqrt{4*2922}=\sqrt{4}*\sqrt{2922}=2\sqrt{2922}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2922}}{2*3}=\frac{0-2\sqrt{2922}}{6}
=-\frac{2\sqrt{2922}}{6}
=-\frac{\sqrt{2922}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2922}}{2*3}=\frac{0+2\sqrt{2922}}{6}
=\frac{2\sqrt{2922}}{6}
=\frac{\sqrt{2922}}{3}
$