(9t-9t2)+15(7t+5)=t

Solution for (9t-9t2)+15(7t+5)=t equation:

(9t-9t^2)+15(7t+5)=t

We move all terms to the left:

(9t-9t^2)+15(7t+5)-(t)=0

We add all the numbers together, and all the variables

(9t-9t^2)-1t+15(7t+5)=0

We multiply parentheses

(9t-9t^2)-1t+105t+75=0

We get rid of parentheses

-9t^2+9t-1t+105t+75=0

We add all the numbers together, and all the variables

-9t^2+113t+75=0

a = -9; b = 113; c = +75;
Δ = b2-4ac
Δ = 1132-4·(-9)·75
Δ = 15469
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{-(113)-\sqrt{15469}}{2*-9}=\frac{-113-\sqrt{15469}}{-18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(113)+\sqrt{15469}}{2*-9}=\frac{-113+\sqrt{15469}}{-18}
$