-3/8x-3=4/3x+11

Solution for -3/8x-3=4/3x+11 equation:

-3/8x-3=4/3x+11

We move all terms to the left:

-3/8x-3-(4/3x+11)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 3x+11)!=0

x∈R


We get rid of parentheses

-3/8x-4/3x-11-3=0

We calculate fractions


(-9x)/24x^2+(-32x)/24x^2-11-3=0

We add all the numbers together, and all the variables

(-9x)/24x^2+(-32x)/24x^2-14=0

We multiply all the terms by the denominator


(-9x)+(-32x)-14*24x^2=0

Wy multiply elements

-336x^2+(-9x)+(-32x)=0

We get rid of parentheses

-336x^2-9x-32x=0

We add all the numbers together, and all the variables

-336x^2-41x=0

a = -336; b = -41; c = 0;
Δ = b2-4ac
Δ = -412-4·(-336)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-41}{2*-336}=\frac{0}{-672}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+41}{2*-336}=\frac{82}{-672}
=-41/336
$