(16x)(9x+16)=133

Solution for (16x)(9x+16)=133 equation:

(16x)(9x+16)=133

We move all terms to the left:

(16x)(9x+16)-(133)=0

We multiply parentheses

144x^2+256x-133=0

a = 144; b = 256; c = -133;
Δ = b2-4ac
Δ = 2562-4·144·(-133)
Δ = 142144
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:

$\sqrt{\Delta}=\sqrt{142144}=\sqrt{64*2221}=\sqrt{64}*\sqrt{2221}=8\sqrt{2221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(256)-8\sqrt{2221}}{2*144}=\frac{-256-8\sqrt{2221}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(256)+8\sqrt{2221}}{2*144}=\frac{-256+8\sqrt{2221}}{288}
$