7/10a+3/2=3/5a+2

Solution for 7/10a+3/2=3/5a+2 equation:

7/10a+3/2=3/5a+2

We move all terms to the left:

7/10a+3/2-(3/5a+2)=0


Domain of the equation: 10a!=0

a!=0/10

a!=0

a∈R



Domain of the equation: 5a+2)!=0

a∈R


We get rid of parentheses

7/10a-3/5a-2+3/2=0

We calculate fractions


750a^2/200a^2+140a/200a^2+(-120a)/200a^2-2=0

We multiply all the terms by the denominator


750a^2+140a+(-120a)-2*200a^2=0

Wy multiply elements

750a^2-400a^2+140a+(-120a)=0

We get rid of parentheses

750a^2-400a^2+140a-120a=0

We add all the numbers together, and all the variables

350a^2+20a=0

a = 350; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·350·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*350}=\frac{-40}{700}
=-2/35
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*350}=\frac{0}{700}
=0
$