76+(12x+14)+(1/5x)=180

Solution for 76+(12x+14)+(1/5x)=180 equation:

76+(12x+14)+(1/5x)=180

We move all terms to the left:

76+(12x+14)+(1/5x)-(180)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(12x+14)+(+1/5x)+76-180=0

We add all the numbers together, and all the variables

(12x+14)+(+1/5x)-104=0

We get rid of parentheses

12x+1/5x+14-104=0

We multiply all the terms by the denominator


12x*5x+14*5x-104*5x+1=0

Wy multiply elements

60x^2+70x-520x+1=0

We add all the numbers together, and all the variables

60x^2-450x+1=0

a = 60; b = -450; c = +1;
Δ = b2-4ac
Δ = -4502-4·60·1
Δ = 202260
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:

$\sqrt{\Delta}=\sqrt{202260}=\sqrt{4*50565}=\sqrt{4}*\sqrt{50565}=2\sqrt{50565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-2\sqrt{50565}}{2*60}=\frac{450-2\sqrt{50565}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+2\sqrt{50565}}{2*60}=\frac{450+2\sqrt{50565}}{120}
$