2x=5x2-6

Solution for 2x=5x2-6 equation:

2x=5x^2-6

We move all terms to the left:

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

We get rid of parentheses

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

a = -5; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-5)·6
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{31}}{2*-5}=\frac{-2-2\sqrt{31}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{31}}{2*-5}=\frac{-2+2\sqrt{31}}{-10}
$