5a=3/4a-3

Solution for 5a=3/4a-3 equation:

5a=3/4a-3

We move all terms to the left:

5a-(3/4a-3)=0


Domain of the equation: 4a-3)!=0

a∈R


We get rid of parentheses

5a-3/4a+3=0

We multiply all the terms by the denominator


5a*4a+3*4a-3=0

Wy multiply elements

20a^2+12a-3=0

a = 20; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·20·(-3)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{6}}{2*20}=\frac{-12-8\sqrt{6}}{40}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{6}}{2*20}=\frac{-12+8\sqrt{6}}{40}
$