9x^2+3=6x^2+78

Solution for 9x^2+3=6x^2+78 equation:

9x^2+3=6x^2+78

We move all terms to the left:

9x^2+3-(6x^2+78)=0

We get rid of parentheses

9x^2-6x^2-78+3=0

We add all the numbers together, and all the variables

3x^2-75=0

a = 3; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·3·(-75)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*3}=\frac{30}{6}
=5
$