76/5x-1x=20

Solution for 76/5x-1x=20 equation:

76/5x-1x=20

We move all terms to the left:

76/5x-1x-(20)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+76/5x-20=0

We multiply all the terms by the denominator


-1x*5x-20*5x+76=0

Wy multiply elements

-5x^2-100x+76=0

a = -5; b = -100; c = +76;
Δ = b2-4ac
Δ = -1002-4·(-5)·76
Δ = 11520
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:

$\sqrt{\Delta}=\sqrt{11520}=\sqrt{2304*5}=\sqrt{2304}*\sqrt{5}=48\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-48\sqrt{5}}{2*-5}=\frac{100-48\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+48\sqrt{5}}{2*-5}=\frac{100+48\sqrt{5}}{-10}
$