2x+2=5x^2-10x+6

Solution for 2x+2=5x^2-10x+6 equation:

2x+2=5x^2-10x+6

We move all terms to the left:

2x+2-(5x^2-10x+6)=0

We get rid of parentheses

-5x^2+2x+10x-6+2=0

We add all the numbers together, and all the variables

-5x^2+12x-4=0

a = -5; b = 12; c = -4;
Δ = b2-4ac
Δ = 122-4·(-5)·(-4)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*-5}=\frac{-20}{-10}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*-5}=\frac{-4}{-10}
=2/5
$