9a=-10+2/5a

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

9a=-10+2/5a

We move all terms to the left:

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


Domain of the equation: 5a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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}
$