5a-13=-1/2a-2

Solution for 5a-13=-1/2a-2 equation:

5a-13=-1/2a-2

We move all terms to the left:

5a-13-(-1/2a-2)=0


Domain of the equation: 2a-2)!=0

a∈R


We get rid of parentheses

5a+1/2a+2-13=0

We multiply all the terms by the denominator


5a*2a+2*2a-13*2a+1=0

Wy multiply elements

10a^2+4a-26a+1=0

We add all the numbers together, and all the variables

10a^2-22a+1=0

a = 10; b = -22; c = +1;
Δ = b2-4ac
Δ = -222-4·10·1
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{111}}{2*10}=\frac{22-2\sqrt{111}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{111}}{2*10}=\frac{22+2\sqrt{111}}{20}
$