5t-6/3t=1

Solution for 5t-6/3t=1 equation:

5t-6/3t=1

We move all terms to the left:

5t-6/3t-(1)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We multiply all the terms by the denominator


5t*3t-1*3t-6=0

Wy multiply elements

15t^2-3t-6=0

a = 15; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·15·(-6)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{41}}{2*15}=\frac{3-3\sqrt{41}}{30}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{41}}{2*15}=\frac{3+3\sqrt{41}}{30}
$