6/9*x=560

Solution for 6/9*x=560 equation:

6/9*x=560

We move all terms to the left:

6/9*x-(560)=0


Domain of the equation: 9*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-560*9*x+6=0

Wy multiply elements

-5040x*x+6=0

Wy multiply elements

-5040x^2+6=0

a = -5040; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-5040)·6
Δ = 120960
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:

$\sqrt{\Delta}=\sqrt{120960}=\sqrt{576*210}=\sqrt{576}*\sqrt{210}=24\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{210}}{2*-5040}=\frac{0-24\sqrt{210}}{-10080}
=-\frac{24\sqrt{210}}{-10080}
=-\frac{\sqrt{210}}{-420}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{210}}{2*-5040}=\frac{0+24\sqrt{210}}{-10080}
=\frac{24\sqrt{210}}{-10080}
=\frac{\sqrt{210}}{-420}
$