-4/5x=5x+6

Solution for -4/5x=5x+6 equation:

-4/5x=5x+6

We move all terms to the left:

-4/5x-(5x+6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-4/5x-5x-6=0

We multiply all the terms by the denominator


-5x*5x-6*5x-4=0

Wy multiply elements

-25x^2-30x-4=0

a = -25; b = -30; c = -4;
Δ = b2-4ac
Δ = -302-4·(-25)·(-4)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{5}}{2*-25}=\frac{30-10\sqrt{5}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{5}}{2*-25}=\frac{30+10\sqrt{5}}{-50}
$