t-4/t=3

Solution for t-4/t=3 equation:

t-4/t=3

We move all terms to the left:

t-4/t-(3)=0


Domain of the equation: t!=0

t∈R


We multiply all the terms by the denominator


t*t-3*t-4=0

We add all the numbers together, and all the variables

-3t+t*t-4=0

Wy multiply elements

t^2-3t-4=0

a = 1; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·1·(-4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*1}=\frac{-2}{2}
=-1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*1}=\frac{8}{2}
=4
$