6x^2+7x+2=4-9x^2

Solution for 6x^2+7x+2=4-9x^2 equation:

6x^2+7x+2=4-9x^2

We move all terms to the left:

6x^2+7x+2-(4-9x^2)=0

We get rid of parentheses

6x^2+9x^2+7x-4+2=0

We add all the numbers together, and all the variables

15x^2+7x-2=0

a = 15; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·15·(-2)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*15}=\frac{-20}{30}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*15}=\frac{6}{30}
=1/5
$