11/4a-9/20a+7/10=4/5

Solution for 11/4a-9/20a+7/10=4/5 equation:

11/4a-9/20a+7/10=4/5

We move all terms to the left:

11/4a-9/20a+7/10-(4/5)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 20a!=0

a!=0/20

a!=0

a∈R


We add all the numbers together, and all the variables

11/4a-9/20a+7/10-(+4/5)=0

We get rid of parentheses

11/4a-9/20a+7/10-4/5=0

We calculate fractions


(-6400a^2)/4000a^2+5600a^2/4000a^2+11000a/4000a^2+(-1800a)/4000a^2=0

We multiply all the terms by the denominator


(-6400a^2)+5600a^2+11000a+(-1800a)=0

We add all the numbers together, and all the variables

5600a^2+(-6400a^2)+11000a+(-1800a)=0

We get rid of parentheses

5600a^2-6400a^2+11000a-1800a=0

We add all the numbers together, and all the variables

-800a^2+9200a=0

a = -800; b = 9200; c = 0;
Δ = b2-4ac
Δ = 92002-4·(-800)·0
Δ = 84640000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{84640000}=9200$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9200)-9200}{2*-800}=\frac{-18400}{-1600}
=11+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9200)+9200}{2*-800}=\frac{0}{-1600}
=0
$