-11/2a-7/5a=-29/30

Solution for -11/2a-7/5a=-29/30 equation:

-11/2a-7/5a=-29/30

We move all terms to the left:

-11/2a-7/5a-(-29/30)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We get rid of parentheses

-11/2a-7/5a+29/30=0

We calculate fractions


1450a^2/900a^2+(-4950a)/900a^2+(-1260a)/900a^2=0

We multiply all the terms by the denominator


1450a^2+(-4950a)+(-1260a)=0

We get rid of parentheses

1450a^2-4950a-1260a=0

We add all the numbers together, and all the variables

1450a^2-6210a=0

a = 1450; b = -6210; c = 0;
Δ = b2-4ac
Δ = -62102-4·1450·0
Δ = 38564100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38564100}=6210$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6210)-6210}{2*1450}=\frac{0}{2900}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6210)+6210}{2*1450}=\frac{12420}{2900}
=4+41/145
$