3t-5/7t+1=-9

Solution for 3t-5/7t+1=-9 equation:

3t-5/7t+1=-9

We move all terms to the left:

3t-5/7t+1-(-9)=0


Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R


We add all the numbers together, and all the variables

3t-5/7t+10=0

We multiply all the terms by the denominator


3t*7t+10*7t-5=0

Wy multiply elements

21t^2+70t-5=0

a = 21; b = 70; c = -5;
Δ = b2-4ac
Δ = 702-4·21·(-5)
Δ = 5320
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:

$\sqrt{\Delta}=\sqrt{5320}=\sqrt{4*1330}=\sqrt{4}*\sqrt{1330}=2\sqrt{1330}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1330}}{2*21}=\frac{-70-2\sqrt{1330}}{42}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1330}}{2*21}=\frac{-70+2\sqrt{1330}}{42}
$