x+7=-4/5x-2

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

x+7=-4/5x-2

We move all terms to the left:

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


Domain of the equation: 5x-2)!=0

x∈R


We get rid of parentheses

x+4/5x+2+7=0

We multiply all the terms by the denominator


x*5x+2*5x+7*5x+4=0

Wy multiply elements

5x^2+10x+35x+4=0

We add all the numbers together, and all the variables

5x^2+45x+4=0

a = 5; b = 45; c = +4;
Δ = b2-4ac
Δ = 452-4·5·4
Δ = 1945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{1945}}{2*5}=\frac{-45-\sqrt{1945}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{1945}}{2*5}=\frac{-45+\sqrt{1945}}{10}
$