51/10a-11=5a-9

Solution for 51/10a-11=5a-9 equation:

51/10a-11=5a-9

We move all terms to the left:

51/10a-11-(5a-9)=0


Domain of the equation: 10a!=0

a!=0/10

a!=0

a∈R


We get rid of parentheses

51/10a-5a+9-11=0

We multiply all the terms by the denominator


-5a*10a+9*10a-11*10a+51=0

Wy multiply elements

-50a^2+90a-110a+51=0

We add all the numbers together, and all the variables

-50a^2-20a+51=0

a = -50; b = -20; c = +51;
Δ = b2-4ac
Δ = -202-4·(-50)·51
Δ = 10600
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:

$\sqrt{\Delta}=\sqrt{10600}=\sqrt{100*106}=\sqrt{100}*\sqrt{106}=10\sqrt{106}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{106}}{2*-50}=\frac{20-10\sqrt{106}}{-100}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{106}}{2*-50}=\frac{20+10\sqrt{106}}{-100}
$