7/2a-28=1/10a-11

Solution for 7/2a-28=1/10a-11 equation:

7/2a-28=1/10a-11

We move all terms to the left:

7/2a-28-(1/10a-11)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 10a-11)!=0

a∈R


We get rid of parentheses

7/2a-1/10a+11-28=0

We calculate fractions


70a/20a^2+(-2a)/20a^2+11-28=0

We add all the numbers together, and all the variables

70a/20a^2+(-2a)/20a^2-17=0

We multiply all the terms by the denominator


70a+(-2a)-17*20a^2=0

Wy multiply elements

-340a^2+70a+(-2a)=0

We get rid of parentheses

-340a^2+70a-2a=0

We add all the numbers together, and all the variables

-340a^2+68a=0

a = -340; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·(-340)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*-340}=\frac{-136}{-680}
=1/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*-340}=\frac{0}{-680}
=0
$