-3/5x-3=-6x+24

Solution for -3/5x-3=-6x+24 equation:

-3/5x-3=-6x+24

We move all terms to the left:

-3/5x-3-(-6x+24)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-3/5x+6x-24-3=0

We multiply all the terms by the denominator


6x*5x-24*5x-3*5x-3=0

Wy multiply elements

30x^2-120x-15x-3=0

We add all the numbers together, and all the variables

30x^2-135x-3=0

a = 30; b = -135; c = -3;
Δ = b2-4ac
Δ = -1352-4·30·(-3)
Δ = 18585
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:

$\sqrt{\Delta}=\sqrt{18585}=\sqrt{9*2065}=\sqrt{9}*\sqrt{2065}=3\sqrt{2065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-3\sqrt{2065}}{2*30}=\frac{135-3\sqrt{2065}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+3\sqrt{2065}}{2*30}=\frac{135+3\sqrt{2065}}{60}
$