7/10a+4-1/2a=5

Solution for 7/10a+4-1/2a=5 equation:

7/10a+4-1/2a=5

We move all terms to the left:

7/10a+4-1/2a-(5)=0


Domain of the equation: 10a!=0

a!=0/10

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

7/10a-1/2a-1=0

We calculate fractions


14a/20a^2+(-10a)/20a^2-1=0

We multiply all the terms by the denominator


14a+(-10a)-1*20a^2=0

Wy multiply elements

-20a^2+14a+(-10a)=0

We get rid of parentheses

-20a^2+14a-10a=0

We add all the numbers together, and all the variables

-20a^2+4a=0

a = -20; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-20)·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*-20}=\frac{-8}{-40}
=1/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-20}=\frac{0}{-40}
=0
$