-10+2/5a=9a

Solution for -10+2/5a=9a equation:

-10+2/5a=9a

We move all terms to the left:

-10+2/5a-(9a)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

-9a+2/5a-10=0

We multiply all the terms by the denominator


-9a*5a-10*5a+2=0

Wy multiply elements

-45a^2-50a+2=0

a = -45; b = -50; c = +2;
Δ = b2-4ac
Δ = -502-4·(-45)·2
Δ = 2860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2860}=\sqrt{4*715}=\sqrt{4}*\sqrt{715}=2\sqrt{715}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{715}}{2*-45}=\frac{50-2\sqrt{715}}{-90}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{715}}{2*-45}=\frac{50+2\sqrt{715}}{-90}
$