/5x+8=11+2x

Solution for /5x+8=11+2x equation:

/5x+8=11+2x

We move all terms to the left:

/5x+8-(11+2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

/5x-(2x+11)+8=0

We get rid of parentheses

/5x-2x-11+8=0

We multiply all the terms by the denominator


-2x*5x-11*5x+8*5x+=0

We add all the numbers together, and all the variables

-2x*5x-11*5x+8*5x=0

Wy multiply elements

-10x^2-55x+40x=0

We add all the numbers together, and all the variables

-10x^2-15x=0

a = -10; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-10)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-10}=\frac{30}{-20}
=-1+1/2
$