4/3x-3/8x=-46

Solution for 4/3x-3/8x=-46 equation:

4/3x-3/8x=-46

We move all terms to the left:

4/3x-3/8x-(-46)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-3/8x+46=0

We calculate fractions


32x/24x^2+(-9x)/24x^2+46=0

We multiply all the terms by the denominator


32x+(-9x)+46*24x^2=0

Wy multiply elements

1104x^2+32x+(-9x)=0

We get rid of parentheses

1104x^2+32x-9x=0

We add all the numbers together, and all the variables

1104x^2+23x=0

a = 1104; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·1104·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*1104}=\frac{-46}{2208}
=-1/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*1104}=\frac{0}{2208}
=0
$