4/3t-2.1t-2.3=7.6

Solution for 4/3t-2.1t-2.3=7.6 equation:

4/3t-2.1t-2.3=7.6

We move all terms to the left:

4/3t-2.1t-2.3-(7.6)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

-2.1t+4/3t-9.9=0

We multiply all the terms by the denominator


-(2.1t)*3t-(9.9)*3t+4=0

We add all the numbers together, and all the variables

-(+2.1t)*3t-(9.9)*3t+4=0

We multiply parentheses

-6t^2-29.7t+4=0

a = -6; b = -29.7; c = +4;
Δ = b2-4ac
Δ = -29.72-4·(-6)·4
Δ = 978.09
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{-(-29.7)-\sqrt{978.09}}{2*-6}=\frac{29.7-\sqrt{978.09}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29.7)+\sqrt{978.09}}{2*-6}=\frac{29.7+\sqrt{978.09}}{-12}
$