4/5x+7=x+9

Solution for 4/5x+7=x+9 equation:

4/5x+7=x+9

We move all terms to the left:

4/5x+7-(x+9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-x-9+7=0

We multiply all the terms by the denominator


-x*5x-9*5x+7*5x+4=0

Wy multiply elements

-5x^2-45x+35x+4=0

We add all the numbers together, and all the variables

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

a = -5; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·(-5)·4
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{5}}{2*-5}=\frac{10-6\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{5}}{2*-5}=\frac{10+6\sqrt{5}}{-10}
$