8t-3/2t+5=-19

Solution for 8t-3/2t+5=-19 equation:

8t-3/2t+5=-19

We move all terms to the left:

8t-3/2t+5-(-19)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We add all the numbers together, and all the variables

8t-3/2t+24=0

We multiply all the terms by the denominator


8t*2t+24*2t-3=0

Wy multiply elements

16t^2+48t-3=0

a = 16; b = 48; c = -3;
Δ = b2-4ac
Δ = 482-4·16·(-3)
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{39}}{2*16}=\frac{-48-8\sqrt{39}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{39}}{2*16}=\frac{-48+8\sqrt{39}}{32}
$