1/5x-4(2x+3)=12

Solution for 1/5x-4(2x+3)=12 equation:

1/5x-4(2x+3)=12

We move all terms to the left:

1/5x-4(2x+3)-(12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply parentheses

1/5x-8x-12-12=0

We multiply all the terms by the denominator


-8x*5x-12*5x-12*5x+1=0

Wy multiply elements

-40x^2-60x-60x+1=0

We add all the numbers together, and all the variables

-40x^2-120x+1=0

a = -40; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·(-40)·1
Δ = 14560
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:

$\sqrt{\Delta}=\sqrt{14560}=\sqrt{16*910}=\sqrt{16}*\sqrt{910}=4\sqrt{910}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{910}}{2*-40}=\frac{120-4\sqrt{910}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{910}}{2*-40}=\frac{120+4\sqrt{910}}{-80}
$