9x2-6+2(3x2-7)=433.75

Solution for 9x2-6+2(3x2-7)=433.75 equation:

9x^2-6+2(3x^2-7)=433.75

We move all terms to the left:

9x^2-6+2(3x^2-7)-(433.75)=0

We add all the numbers together, and all the variables

9x^2+2(3x^2-7)-439.75=0

We multiply parentheses

9x^2+6x^2-14-439.75=0

We add all the numbers together, and all the variables

15x^2-453.75=0

a = 15; b = 0; c = -453.75;
Δ = b2-4ac
Δ = 02-4·15·(-453.75)
Δ = 27225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27225}=165$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-165}{2*15}=\frac{-165}{30}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+165}{2*15}=\frac{165}{30}
=5+1/2
$