4/5x+10=-5/4x+33

Solution for 4/5x+10=-5/4x+33 equation:

4/5x+10=-5/4x+33

We move all terms to the left:

4/5x+10-(-5/4x+33)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+33)!=0

x∈R


We get rid of parentheses

4/5x+5/4x-33+10=0

We calculate fractions


16x/20x^2+25x/20x^2-33+10=0

We add all the numbers together, and all the variables

16x/20x^2+25x/20x^2-23=0

We multiply all the terms by the denominator


16x+25x-23*20x^2=0

We add all the numbers together, and all the variables

41x-23*20x^2=0

Wy multiply elements

-460x^2+41x=0

a = -460; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-460)·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*-460}=\frac{-82}{-920}
=41/460
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-460}=\frac{0}{-920}
=0
$