4/5a-3/2a=-1

Solution for 4/5a-3/2a=-1 equation:

4/5a-3/2a=-1

We move all terms to the left:

4/5a-3/2a-(-1)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

4/5a-3/2a+1=0

We calculate fractions


8a/10a^2+(-15a)/10a^2+1=0

We multiply all the terms by the denominator


8a+(-15a)+1*10a^2=0

Wy multiply elements

10a^2+8a+(-15a)=0

We get rid of parentheses

10a^2+8a-15a=0

We add all the numbers together, and all the variables

10a^2-7a=0

a = 10; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·10·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*10}=\frac{0}{20}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*10}=\frac{14}{20}
=7/10
$