-6/5x-1.6=-2.9x

Solution for -6/5x-1.6=-2.9x equation:

-6/5x-1.6=-2.9x

We move all terms to the left:

-6/5x-1.6-(-2.9x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-6/5x+2.9x-1.6=0

We multiply all the terms by the denominator


(2.9x)*5x-(1.6)*5x-6=0

We add all the numbers together, and all the variables

(+2.9x)*5x-(1.6)*5x-6=0

We multiply parentheses

10x^2-8x-6=0

a = 10; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·10·(-6)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{19}}{2*10}=\frac{8-4\sqrt{19}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{19}}{2*10}=\frac{8+4\sqrt{19}}{20}
$