/4x+5x-12=42

Solution for /4x+5x-12=42 equation:

/4x+5x-12=42

We move all terms to the left:

/4x+5x-12-(42)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5x+/4x-54=0

We multiply all the terms by the denominator


5x*4x-54*4x+=0

We add all the numbers together, and all the variables

5x*4x-54*4x=0

Wy multiply elements

20x^2-216x=0

a = 20; b = -216; c = 0;
Δ = b2-4ac
Δ = -2162-4·20·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-216}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+216}{2*20}=\frac{432}{40}
=10+4/5
$