7t(t-2)-t=4

Solution for 7t(t-2)-t=4 equation:

7t(t-2)-t=4

We move all terms to the left:

7t(t-2)-t-(4)=0

We add all the numbers together, and all the variables

-1t+7t(t-2)-4=0

We multiply parentheses

7t^2-1t-14t-4=0

We add all the numbers together, and all the variables

7t^2-15t-4=0

a = 7; b = -15; c = -4;
Δ = b2-4ac
Δ = -152-4·7·(-4)
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{337}}{2*7}=\frac{15-\sqrt{337}}{14}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{337}}{2*7}=\frac{15+\sqrt{337}}{14}
$