5x+8/9x+21=180

Solution for 5x+8/9x+21=180 equation:

5x+8/9x+21=180

We move all terms to the left:

5x+8/9x+21-(180)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

5x+8/9x-159=0

We multiply all the terms by the denominator


5x*9x-159*9x+8=0

Wy multiply elements

45x^2-1431x+8=0

a = 45; b = -1431; c = +8;
Δ = b2-4ac
Δ = -14312-4·45·8
Δ = 2046321
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:

$\sqrt{\Delta}=\sqrt{2046321}=\sqrt{9*227369}=\sqrt{9}*\sqrt{227369}=3\sqrt{227369}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1431)-3\sqrt{227369}}{2*45}=\frac{1431-3\sqrt{227369}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1431)+3\sqrt{227369}}{2*45}=\frac{1431+3\sqrt{227369}}{90}
$