0=4t^2-6t-475

Solution for 0=4t^2-6t-475 equation:

0=4t^2-6t-475

We move all terms to the left:

0-(4t^2-6t-475)=0

We add all the numbers together, and all the variables

-(4t^2-6t-475)=0

We get rid of parentheses

-4t^2+6t+475=0

a = -4; b = 6; c = +475;
Δ = b2-4ac
Δ = 62-4·(-4)·475
Δ = 7636
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:

$\sqrt{\Delta}=\sqrt{7636}=\sqrt{4*1909}=\sqrt{4}*\sqrt{1909}=2\sqrt{1909}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{1909}}{2*-4}=\frac{-6-2\sqrt{1909}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{1909}}{2*-4}=\frac{-6+2\sqrt{1909}}{-8}
$