(1/7)5x-12x=19

Solution for (1/7)5x-12x=19 equation:

(1/7)5x-12x=19

We move all terms to the left:

(1/7)5x-12x-(19)=0


Domain of the equation: 7)5x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/7)5x-12x-19=0

We add all the numbers together, and all the variables

-12x+(+1/7)5x-19=0

We multiply parentheses

5x^2-12x-19=0

a = 5; b = -12; c = -19;
Δ = b2-4ac
Δ = -122-4·5·(-19)
Δ = 524
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:

$\sqrt{\Delta}=\sqrt{524}=\sqrt{4*131}=\sqrt{4}*\sqrt{131}=2\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{131}}{2*5}=\frac{12-2\sqrt{131}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{131}}{2*5}=\frac{12+2\sqrt{131}}{10}
$