9x^2-16+8x^2-6x=0

Solution for 9x^2-16+8x^2-6x=0 equation:

9x^2-16+8x^2-6x=0

We add all the numbers together, and all the variables

17x^2-6x-16=0

a = 17; b = -6; c = -16;
Δ = b2-4ac
Δ = -62-4·17·(-16)
Δ = 1124
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:

$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{281}}{2*17}=\frac{6-2\sqrt{281}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{281}}{2*17}=\frac{6+2\sqrt{281}}{34}
$