9(8x+5)x=0.25

Solution for 9(8x+5)x=0.25 equation:

9(8x+5)x=0.25

We move all terms to the left:

9(8x+5)x-(0.25)=0

We add all the numbers together, and all the variables

9(8x+5)x-0.25=0

We multiply parentheses

72x^2+45x-0.25=0

a = 72; b = 45; c = -0.25;
Δ = b2-4ac
Δ = 452-4·72·(-0.25)
Δ = 2097
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:

$\sqrt{\Delta}=\sqrt{2097}=\sqrt{9*233}=\sqrt{9}*\sqrt{233}=3\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{233}}{2*72}=\frac{-45-3\sqrt{233}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{233}}{2*72}=\frac{-45+3\sqrt{233}}{144}
$