4/5a-3=3/10a+7

Solution for 4/5a-3=3/10a+7 equation:

4/5a-3=3/10a+7

We move all terms to the left:

4/5a-3-(3/10a+7)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 10a+7)!=0

a∈R


We get rid of parentheses

4/5a-3/10a-7-3=0

We calculate fractions


40a/50a^2+(-15a)/50a^2-7-3=0

We add all the numbers together, and all the variables

40a/50a^2+(-15a)/50a^2-10=0

We multiply all the terms by the denominator


40a+(-15a)-10*50a^2=0

Wy multiply elements

-500a^2+40a+(-15a)=0

We get rid of parentheses

-500a^2+40a-15a=0

We add all the numbers together, and all the variables

-500a^2+25a=0

a = -500; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-500)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-500}=\frac{-50}{-1000}
=1/20
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-500}=\frac{0}{-1000}
=0
$