(9x^2-16)=(8x^2-6x)

Solution for (9x^2-16)=(8x^2-6x) equation:

(9x^2-16)=(8x^2-6x)

We move all terms to the left:

(9x^2-16)-((8x^2-6x))=0

We get rid of parentheses

9x^2-((8x^2-6x))-16=0


We calculate terms in parentheses: -((8x^2-6x)), so:

(8x^2-6x)

We get rid of parentheses

8x^2-6x

Back to the equation:

-(8x^2-6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+6x-16=0

a = 1; b = 6; c = -16;
Δ = b2-4ac
Δ = 62-4·1·(-16)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*1}=\frac{4}{2}
=2
$