5t+7=3/2t-14

Solution for 5t+7=3/2t-14 equation:

5t+7=3/2t-14

We move all terms to the left:

5t+7-(3/2t-14)=0


Domain of the equation: 2t-14)!=0

t∈R


We get rid of parentheses

5t-3/2t+14+7=0

We multiply all the terms by the denominator


5t*2t+14*2t+7*2t-3=0

Wy multiply elements

10t^2+28t+14t-3=0

We add all the numbers together, and all the variables

10t^2+42t-3=0

a = 10; b = 42; c = -3;
Δ = b2-4ac
Δ = 422-4·10·(-3)
Δ = 1884
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:

$\sqrt{\Delta}=\sqrt{1884}=\sqrt{4*471}=\sqrt{4}*\sqrt{471}=2\sqrt{471}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{471}}{2*10}=\frac{-42-2\sqrt{471}}{20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{471}}{2*10}=\frac{-42+2\sqrt{471}}{20}
$