x+6=5x^2-3x+2

Solution for x+6=5x^2-3x+2 equation:

x+6=5x^2-3x+2

We move all terms to the left:

x+6-(5x^2-3x+2)=0

We get rid of parentheses

-5x^2+x+3x-2+6=0

We add all the numbers together, and all the variables

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

a = -5; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-5)·4
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*-5}=\frac{-4-4\sqrt{6}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*-5}=\frac{-4+4\sqrt{6}}{-10}
$