5x-10=10(1/4x+12)

Solution for 5x-10=10(1/4x+12) equation:

5x-10=10(1/4x+12)

We move all terms to the left:

5x-10-(10(1/4x+12))=0


Domain of the equation: 4x+12))!=0

x∈R


We multiply all the terms by the denominator


5x*4x-10*4x+12))-(10(1+12))=0

We add all the numbers together, and all the variables

5x*4x-10*4x+12))-(1013)=0

We add all the numbers together, and all the variables

5x*4x-10*4x=0

Wy multiply elements

20x^2-40x=0

a = 20; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·20·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*20}=\frac{80}{40}
=2
$