6x+4=5x2+2.

Solution for 6x+4=5x2+2. equation:

6x+4=5x^2+2.

We move all terms to the left:

6x+4-(5x^2+2.)=0

We get rid of parentheses

-5x^2+6x-2.+4=0

We add all the numbers together, and all the variables

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

a = -5; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-5)·2
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{19}}{2*-5}=\frac{-6-2\sqrt{19}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{19}}{2*-5}=\frac{-6+2\sqrt{19}}{-10}
$