5x2=5x+2

Solution for 5x2=5x+2 equation:

5x^2=5x+2

We move all terms to the left:

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

We get rid of parentheses

5x^2-5x-2=0

a = 5; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·5·(-2)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{65}}{2*5}=\frac{5-\sqrt{65}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*5}=\frac{5+\sqrt{65}}{10}
$