-x-4=3/5x+4

Solution for -x-4=3/5x+4 equation:

-x-4=3/5x+4

We move all terms to the left:

-x-4-(3/5x+4)=0


Domain of the equation: 5x+4)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(3/5x+4)-4=0

We get rid of parentheses

-1x-3/5x-4-4=0

We multiply all the terms by the denominator


-1x*5x-4*5x-4*5x-3=0

Wy multiply elements

-5x^2-20x-20x-3=0

We add all the numbers together, and all the variables

-5x^2-40x-3=0

a = -5; b = -40; c = -3;
Δ = b2-4ac
Δ = -402-4·(-5)·(-3)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{385}}{2*-5}=\frac{40-2\sqrt{385}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{385}}{2*-5}=\frac{40+2\sqrt{385}}{-10}
$