4/9x+4=-5x-3

Solution for 4/9x+4=-5x-3 equation:

4/9x+4=-5x-3

We move all terms to the left:

4/9x+4-(-5x-3)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

4/9x+5x+3+4=0

We multiply all the terms by the denominator


5x*9x+3*9x+4*9x+4=0

Wy multiply elements

45x^2+27x+36x+4=0

We add all the numbers together, and all the variables

45x^2+63x+4=0

a = 45; b = 63; c = +4;
Δ = b2-4ac
Δ = 632-4·45·4
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-57}{2*45}=\frac{-120}{90}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+57}{2*45}=\frac{-6}{90}
=-1/15
$