4/5x-15=3x+3

Solution for 4/5x-15=3x+3 equation:

4/5x-15=3x+3

We move all terms to the left:

4/5x-15-(3x+3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-3x-3-15=0

We multiply all the terms by the denominator


-3x*5x-3*5x-15*5x+4=0

Wy multiply elements

-15x^2-15x-75x+4=0

We add all the numbers together, and all the variables

-15x^2-90x+4=0

a = -15; b = -90; c = +4;
Δ = b2-4ac
Δ = -902-4·(-15)·4
Δ = 8340
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:

$\sqrt{\Delta}=\sqrt{8340}=\sqrt{4*2085}=\sqrt{4}*\sqrt{2085}=2\sqrt{2085}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2085}}{2*-15}=\frac{90-2\sqrt{2085}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2085}}{2*-15}=\frac{90+2\sqrt{2085}}{-30}
$