x+5/9(x)=140

Solution for x+5/9(x)=140 equation:

x+5/9(x)=140

We move all terms to the left:

x+5/9(x)-(140)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


x*9x-140*9x+5=0

Wy multiply elements

9x^2-1260x+5=0

a = 9; b = -1260; c = +5;
Δ = b2-4ac
Δ = -12602-4·9·5
Δ = 1587420
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:

$\sqrt{\Delta}=\sqrt{1587420}=\sqrt{36*44095}=\sqrt{36}*\sqrt{44095}=6\sqrt{44095}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1260)-6\sqrt{44095}}{2*9}=\frac{1260-6\sqrt{44095}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1260)+6\sqrt{44095}}{2*9}=\frac{1260+6\sqrt{44095}}{18}
$