120=10t^2-46t+120

Solution for 120=10t^2-46t+120 equation:

120=10t^2-46t+120

We move all terms to the left:

120-(10t^2-46t+120)=0

We get rid of parentheses

-10t^2+46t-120+120=0

We add all the numbers together, and all the variables

-10t^2+46t=0

a = -10; b = 46; c = 0;
Δ = b2-4ac
Δ = 462-4·(-10)·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-46}{2*-10}=\frac{-92}{-20}
=4+3/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+46}{2*-10}=\frac{0}{-20}
=0
$