x+2/3=-2(4/5x-7)

Solution for x+2/3=-2(4/5x-7) equation:

x+2/3=-2(4/5x-7)

We move all terms to the left:

x+2/3-(-2(4/5x-7))=0


Domain of the equation: 5x-7))!=0

x∈R


We calculate fractions


x+()/5x+10x/5x=0

We multiply all the terms by the denominator


x*5x+10x+()=0

We add all the numbers together, and all the variables

10x+x*5x=0

Wy multiply elements

5x^2+10x=0

a = 5; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·5·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*5}=\frac{0}{10}
=0
$