4t(-7t+19)=0

Solution for 4t(-7t+19)=0 equation:

4t(-7t+19)=0

We multiply parentheses

-28t^2+76t=0

a = -28; b = 76; c = 0;
Δ = b2-4ac
Δ = 762-4·(-28)·0
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-76}{2*-28}=\frac{-152}{-56}
=2+5/7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+76}{2*-28}=\frac{0}{-56}
=0
$