6x=2-5x^2

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

6x=2-5x^2

We move all terms to the left:

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

We get rid of parentheses

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}
$