9x(5/6)=40

Solution for 9x(5/6)=40 equation:

9x(5/6)=40

We move all terms to the left:

9x(5/6)-(40)=0

We add all the numbers together, and all the variables

9x(+5/6)-40=0

We multiply parentheses

45x^2-40=0

a = 45; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·45·(-40)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*45}=\frac{0-60\sqrt{2}}{90}
=-\frac{60\sqrt{2}}{90}
=-\frac{2\sqrt{2}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*45}=\frac{0+60\sqrt{2}}{90}
=\frac{60\sqrt{2}}{90}
=\frac{2\sqrt{2}}{3}
$