-48/7x=3x+57

Solution for -48/7x=3x+57 equation:

-48/7x=3x+57

We move all terms to the left:

-48/7x-(3x+57)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

-48/7x-3x-57=0

We multiply all the terms by the denominator


-3x*7x-57*7x-48=0

Wy multiply elements

-21x^2-399x-48=0

a = -21; b = -399; c = -48;
Δ = b2-4ac
Δ = -3992-4·(-21)·(-48)
Δ = 155169
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:

$\sqrt{\Delta}=\sqrt{155169}=\sqrt{9*17241}=\sqrt{9}*\sqrt{17241}=3\sqrt{17241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-399)-3\sqrt{17241}}{2*-21}=\frac{399-3\sqrt{17241}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-399)+3\sqrt{17241}}{2*-21}=\frac{399+3\sqrt{17241}}{-42}
$