3t+2/2t-7=0

Solution for 3t+2/2t-7=0 equation:

3t+2/2t-7=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We multiply all the terms by the denominator


3t*2t-7*2t+2=0

Wy multiply elements

6t^2-14t+2=0

a = 6; b = -14; c = +2;
Δ = b2-4ac
Δ = -142-4·6·2
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{37}}{2*6}=\frac{14-2\sqrt{37}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{37}}{2*6}=\frac{14+2\sqrt{37}}{12}
$