-6(x^2-9)=4x^2-146

Solution for -6(x^2-9)=4x^2-146 equation:

-6(x^2-9)=4x^2-146

We move all terms to the left:

-6(x^2-9)-(4x^2-146)=0

We multiply parentheses

-6x^2-(4x^2-146)+54=0

We get rid of parentheses

-6x^2-4x^2+146+54=0

We add all the numbers together, and all the variables

-10x^2+200=0

a = -10; b = 0; c = +200;
Δ = b2-4ac
Δ = 02-4·(-10)·200
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5}}{2*-10}=\frac{0-40\sqrt{5}}{-20}
=-\frac{40\sqrt{5}}{-20}
=-\frac{2\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5}}{2*-10}=\frac{0+40\sqrt{5}}{-20}
=\frac{40\sqrt{5}}{-20}
=\frac{2\sqrt{5}}{-1}
$