3x-2=16x^2-24+9

Solution for 3x-2=16x^2-24+9 equation:

3x-2=16x^2-24+9

We move all terms to the left:

3x-2-(16x^2-24+9)=0

We get rid of parentheses

-16x^2+3x+24-9-2=0

We add all the numbers together, and all the variables

-16x^2+3x+13=0

a = -16; b = 3; c = +13;
Δ = b2-4ac
Δ = 32-4·(-16)·13
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-29}{2*-16}=\frac{-32}{-32}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+29}{2*-16}=\frac{26}{-32}
=-13/16
$