-4x^2=6x^2-9

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

-4x^2=6x^2-9

We move all terms to the left:

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

We get rid of parentheses

-4x^2-6x^2+9=0

We add all the numbers together, and all the variables

-10x^2+9=0

a = -10; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-10)·9
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*-10}=\frac{0-6\sqrt{10}}{-20}
=-\frac{6\sqrt{10}}{-20}
=-\frac{3\sqrt{10}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*-10}=\frac{0+6\sqrt{10}}{-20}
=\frac{6\sqrt{10}}{-20}
=\frac{3\sqrt{10}}{-10}
$