2-2x=3/4x+13

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

2-2x=3/4x+13

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-8x^2-44x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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