4/5a+9/10a=6

Solution for 4/5a+9/10a=6 equation:

4/5a+9/10a=6

We move all terms to the left:

4/5a+9/10a-(6)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 10a!=0

a!=0/10

a!=0

a∈R


We calculate fractions


40a/50a^2+45a/50a^2-6=0

We multiply all the terms by the denominator


40a+45a-6*50a^2=0

We add all the numbers together, and all the variables

85a-6*50a^2=0

Wy multiply elements

-300a^2+85a=0

a = -300; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·(-300)·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*-300}=\frac{-170}{-600}
=17/60
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*-300}=\frac{0}{-600}
=0
$