9t+6=3t+4/9t-4=3t-4

Solution for 9t+6=3t+4/9t-4=3t-4 equation:

9t+6=3t+4/9t-4=3t-4

We move all terms to the left:

9t+6-(3t+4/9t-4)=0


Domain of the equation: 9t-4)!=0

t∈R


We get rid of parentheses

9t-3t-4/9t+4+6=0

We multiply all the terms by the denominator


9t*9t-3t*9t+4*9t+6*9t-4=0

Wy multiply elements

81t^2-27t^2+36t+54t-4=0

We add all the numbers together, and all the variables

54t^2+90t-4=0

a = 54; b = 90; c = -4;
Δ = b2-4ac
Δ = 902-4·54·(-4)
Δ = 8964
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:

$\sqrt{\Delta}=\sqrt{8964}=\sqrt{36*249}=\sqrt{36}*\sqrt{249}=6\sqrt{249}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{249}}{2*54}=\frac{-90-6\sqrt{249}}{108}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{249}}{2*54}=\frac{-90+6\sqrt{249}}{108}
$