(5/13t)*(13t)=-9*13t

Solution for (5/13t)*(13t)=-9*13t equation:

(5/13t)(13t)=-9*13t

We move all terms to the left:

(5/13t)(13t)-(-9*13t)=0


Domain of the equation: 13t)13t!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

(+5/13t)13t-(-9*13t)=0

We multiply parentheses

65t^2-(-9*13t)=0

We get rid of parentheses

65t^2+9*13t=0

Wy multiply elements

65t^2+117t=0

a = 65; b = 117; c = 0;
Δ = b2-4ac
Δ = 1172-4·65·0
Δ = 13689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13689}=117$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(117)-117}{2*65}=\frac{-234}{130}
=-1+4/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(117)+117}{2*65}=\frac{0}{130}
=0
$