2=5x^2+9x+6

Solution for 2=5x^2+9x+6 equation:

2=5x^2+9x+6

We move all terms to the left:

2-(5x^2+9x+6)=0

We get rid of parentheses

-5x^2-9x-6+2=0

We add all the numbers together, and all the variables

-5x^2-9x-4=0

a = -5; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·(-5)·(-4)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*-5}=\frac{8}{-10}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*-5}=\frac{10}{-10}
=-1
$