2-2a=3/4a+13

Solution for 2-2a=3/4a+13 equation:

2-2a=3/4a+13

We move all terms to the left:

2-2a-(3/4a+13)=0


Domain of the equation: 4a+13)!=0

a∈R


We get rid of parentheses

-2a-3/4a-13+2=0

We multiply all the terms by the denominator


-2a*4a-13*4a+2*4a-3=0

Wy multiply elements

-8a^2-52a+8a-3=0

We add all the numbers together, and all the variables

-8a^2-44a-3=0

a = -8; b = -44; c = -3;
Δ = b2-4ac
Δ = -442-4·(-8)·(-3)
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{115}}{2*-8}=\frac{44-4\sqrt{115}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{115}}{2*-8}=\frac{44+4\sqrt{115}}{-16}
$