5-x=7+4/5x

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

5-x=7+4/5x

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x-(4/5x+7)+5=0

We get rid of parentheses

-1x-4/5x-7+5=0

We multiply all the terms by the denominator


-1x*5x-7*5x+5*5x-4=0

Wy multiply elements

-5x^2-35x+25x-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 = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{5}}{2*-5}=\frac{10-2\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{5}}{2*-5}=\frac{10+2\sqrt{5}}{-10}
$