6t^2+30=41t

Solution for 6t^2+30=41t equation:

6t^2+30=41t

We move all terms to the left:

6t^2+30-(41t)=0

a = 6; b = -41; c = +30;
Δ = b2-4ac
Δ = -412-4·6·30
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-31}{2*6}=\frac{10}{12}
=5/6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+31}{2*6}=\frac{72}{12}
=6
$