-2t=3/2t-7

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

-2t=3/2t-7

We move all terms to the left:

-2t-(3/2t-7)=0


Domain of the equation: 2t-7)!=0

t∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4t^2+14t-3=0

a = -4; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·(-4)·(-3)
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*-4}=\frac{-14-2\sqrt{37}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{37}}{2*-4}=\frac{-14+2\sqrt{37}}{-8}
$