(7t-9t2)=13(7t+3)

Solution for (7t-9t2)=13(7t+3) equation:

(7t-9t^2)=13(7t+3)

We move all terms to the left:

(7t-9t^2)-(13(7t+3))=0

We get rid of parentheses

-9t^2+7t-(13(7t+3))=0


We calculate terms in parentheses: -(13(7t+3)), so:

13(7t+3)

We multiply parentheses

91t+39

Back to the equation:

-(91t+39)


We get rid of parentheses

-9t^2+7t-91t-39=0

We add all the numbers together, and all the variables

-9t^2-84t-39=0

a = -9; b = -84; c = -39;
Δ = b2-4ac
Δ = -842-4·(-9)·(-39)
Δ = 5652
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:

$\sqrt{\Delta}=\sqrt{5652}=\sqrt{36*157}=\sqrt{36}*\sqrt{157}=6\sqrt{157}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-6\sqrt{157}}{2*-9}=\frac{84-6\sqrt{157}}{-18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+6\sqrt{157}}{2*-9}=\frac{84+6\sqrt{157}}{-18}
$