t(10-4.9t)=-300

Solution for t(10-4.9t)=-300 equation:

t(10-4.9t)=-300

We move all terms to the left:

t(10-4.9t)-(-300)=0

We add all the numbers together, and all the variables

t(-4.9t+10)-(-300)=0

We add all the numbers together, and all the variables

t(-4.9t+10)+300=0

We multiply parentheses

-4t^2+10t+300=0

a = -4; b = 10; c = +300;
Δ = b2-4ac
Δ = 102-4·(-4)·300
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-70}{2*-4}=\frac{-80}{-8}
=+10
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+70}{2*-4}=\frac{60}{-8}
=-7+1/2
$