4t+40/3t+30=4

Solution for 4t+40/3t+30=4 equation:

4t+40/3t+30=4

We move all terms to the left:

4t+40/3t+30-(4)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

4t+40/3t+26=0

We multiply all the terms by the denominator


4t*3t+26*3t+40=0

Wy multiply elements

12t^2+78t+40=0

a = 12; b = 78; c = +40;
Δ = b2-4ac
Δ = 782-4·12·40
Δ = 4164
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:

$\sqrt{\Delta}=\sqrt{4164}=\sqrt{4*1041}=\sqrt{4}*\sqrt{1041}=2\sqrt{1041}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1041}}{2*12}=\frac{-78-2\sqrt{1041}}{24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1041}}{2*12}=\frac{-78+2\sqrt{1041}}{24}
$