a-3/2a+4a=0

Solution for a-3/2a+4a=0 equation:

a-3/2a+4a=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

5a-3/2a=0

We multiply all the terms by the denominator


5a*2a-3=0

Wy multiply elements

10a^2-3=0

a = 10; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·10·(-3)
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*10}=\frac{0-2\sqrt{30}}{20}
=-\frac{2\sqrt{30}}{20}
=-\frac{\sqrt{30}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*10}=\frac{0+2\sqrt{30}}{20}
=\frac{2\sqrt{30}}{20}
=\frac{\sqrt{30}}{10}
$