-3(2t-5)/2t=5t=4

Solution for -3(2t-5)/2t=5t=4 equation:

-3(2t-5)/2t=5t=4

We move all terms to the left:

-3(2t-5)/2t-(5t)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We add all the numbers together, and all the variables

-5t-3(2t-5)/2t=0

We multiply all the terms by the denominator


-5t*2t-3(2t-5)=0

We multiply parentheses

-5t*2t-6t+15=0

Wy multiply elements

-10t^2-6t+15=0

a = -10; b = -6; c = +15;
Δ = b2-4ac
Δ = -62-4·(-10)·15
Δ = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{159}}{2*-10}=\frac{6-2\sqrt{159}}{-20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{159}}{2*-10}=\frac{6+2\sqrt{159}}{-20}
$