5x+(8)/(9)x=180

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

5x+(8)/(9)x=180

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


5x*9x-180*9x+8=0

Wy multiply elements

45x^2-1620x+8=0

a = 45; b = -1620; c = +8;
Δ = b2-4ac
Δ = -16202-4·45·8
Δ = 2622960
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:

$\sqrt{\Delta}=\sqrt{2622960}=\sqrt{144*18215}=\sqrt{144}*\sqrt{18215}=12\sqrt{18215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1620)-12\sqrt{18215}}{2*45}=\frac{1620-12\sqrt{18215}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1620)+12\sqrt{18215}}{2*45}=\frac{1620+12\sqrt{18215}}{90}
$