93/5x=3x-3

Solution for 93/5x=3x-3 equation:

93/5x=3x-3

We move all terms to the left:

93/5x-(3x-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

93/5x-3x+3=0

We multiply all the terms by the denominator


-3x*5x+3*5x+93=0

Wy multiply elements

-15x^2+15x+93=0

a = -15; b = 15; c = +93;
Δ = b2-4ac
Δ = 152-4·(-15)·93
Δ = 5805
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:

$\sqrt{\Delta}=\sqrt{5805}=\sqrt{9*645}=\sqrt{9}*\sqrt{645}=3\sqrt{645}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{645}}{2*-15}=\frac{-15-3\sqrt{645}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{645}}{2*-15}=\frac{-15+3\sqrt{645}}{-30}
$