-1/292x-60=4x-24

Solution for -1/292x-60=4x-24 equation:

-1/292x-60=4x-24

We move all terms to the left:

-1/292x-60-(4x-24)=0


Domain of the equation: 292x!=0

x!=0/292

x!=0

x∈R


We get rid of parentheses

-1/292x-4x+24-60=0

We multiply all the terms by the denominator


-4x*292x+24*292x-60*292x-1=0

Wy multiply elements

-1168x^2+7008x-17520x-1=0

We add all the numbers together, and all the variables

-1168x^2-10512x-1=0

a = -1168; b = -10512; c = -1;
Δ = b2-4ac
Δ = -105122-4·(-1168)·(-1)
Δ = 110497472
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:

$\sqrt{\Delta}=\sqrt{110497472}=\sqrt{64*1726523}=\sqrt{64}*\sqrt{1726523}=8\sqrt{1726523}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10512)-8\sqrt{1726523}}{2*-1168}=\frac{10512-8\sqrt{1726523}}{-2336}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10512)+8\sqrt{1726523}}{2*-1168}=\frac{10512+8\sqrt{1726523}}{-2336}
$