5.8/3t+6=38t+4.32

Solution for 5.8/3t+6=38t+4.32 equation:

5.8/3t+6=38t+4.32

We move all terms to the left:

5.8/3t+6-(38t+4.32)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We get rid of parentheses

5.8/3t-38t-4.32+6=0

We multiply all the terms by the denominator


-38t*3t-(4.32)*3t+6*3t+5.8=0

We multiply parentheses

-38t*3t-12.96t+6*3t+5.8=0

Wy multiply elements

-114t^2-12.96t+18t+5.8=0

We add all the numbers together, and all the variables

-114t^2+5.04t+5.8=0

a = -114; b = 5.04; c = +5.8;
Δ = b2-4ac
Δ = 5.042-4·(-114)·5.8
Δ = 2670.2016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5.04)-\sqrt{2670.2016}}{2*-114}=\frac{-5.04-\sqrt{2670.2016}}{-228}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.04)+\sqrt{2670.2016}}{2*-114}=\frac{-5.04+\sqrt{2670.2016}}{-228}
$