4/5x-24x=30

Solution for 4/5x-24x=30 equation:

4/5x-24x=30

We move all terms to the left:

4/5x-24x-(30)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-24x+4/5x-30=0

We multiply all the terms by the denominator


-24x*5x-30*5x+4=0

Wy multiply elements

-120x^2-150x+4=0

a = -120; b = -150; c = +4;
Δ = b2-4ac
Δ = -1502-4·(-120)·4
Δ = 24420
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:

$\sqrt{\Delta}=\sqrt{24420}=\sqrt{4*6105}=\sqrt{4}*\sqrt{6105}=2\sqrt{6105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{6105}}{2*-120}=\frac{150-2\sqrt{6105}}{-240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{6105}}{2*-120}=\frac{150+2\sqrt{6105}}{-240}
$