/8x-12=5x+30

Solution for /8x-12=5x+30 equation:

/8x-12=5x+30

We move all terms to the left:

/8x-12-(5x+30)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

/8x-5x-30-12=0

We multiply all the terms by the denominator


-5x*8x-30*8x-12*8x+=0

We add all the numbers together, and all the variables

-5x*8x-30*8x-12*8x=0

Wy multiply elements

-40x^2-240x-96x=0

We add all the numbers together, and all the variables

-40x^2-336x=0

a = -40; b = -336; c = 0;
Δ = b2-4ac
Δ = -3362-4·(-40)·0
Δ = 112896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{112896}=336$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-336}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+336}{2*-40}=\frac{672}{-80}
=-8+2/5
$