7t(t-4)=25

Solution for 7t(t-4)=25 equation:

7t(t-4)=25

We move all terms to the left:

7t(t-4)-(25)=0

We multiply parentheses

7t^2-28t-25=0

a = 7; b = -28; c = -25;
Δ = b2-4ac
Δ = -282-4·7·(-25)
Δ = 1484
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:

$\sqrt{\Delta}=\sqrt{1484}=\sqrt{4*371}=\sqrt{4}*\sqrt{371}=2\sqrt{371}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{371}}{2*7}=\frac{28-2\sqrt{371}}{14}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{371}}{2*7}=\frac{28+2\sqrt{371}}{14}
$