0=7t^2-54t+35

Solution for 0=7t^2-54t+35 equation:

0=7t^2-54t+35

We move all terms to the left:

0-(7t^2-54t+35)=0

We add all the numbers together, and all the variables

-(7t^2-54t+35)=0

We get rid of parentheses

-7t^2+54t-35=0

a = -7; b = 54; c = -35;
Δ = b2-4ac
Δ = 542-4·(-7)·(-35)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-44}{2*-7}=\frac{-98}{-14}
=+7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+44}{2*-7}=\frac{-10}{-14}
=5/7
$