2/2a-1=3/5a-10

Solution for 2/2a-1=3/5a-10 equation:

2/2a-1=3/5a-10

We move all terms to the left:

2/2a-1-(3/5a-10)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 5a-10)!=0

a∈R


We get rid of parentheses

2/2a-3/5a+10-1=0

We calculate fractions


10a/10a^2+(-6a)/10a^2+10-1=0

We add all the numbers together, and all the variables

10a/10a^2+(-6a)/10a^2+9=0

We multiply all the terms by the denominator


10a+(-6a)+9*10a^2=0

Wy multiply elements

90a^2+10a+(-6a)=0

We get rid of parentheses

90a^2+10a-6a=0

We add all the numbers together, and all the variables

90a^2+4a=0

a = 90; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·90·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*90}=\frac{-8}{180}
=-2/45
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*90}=\frac{0}{180}
=0
$