5x^2+1=2x+13

Solution for 5x^2+1=2x+13 equation:

5x^2+1=2x+13

We move all terms to the left:

5x^2+1-(2x+13)=0

We get rid of parentheses

5x^2-2x-13+1=0

We add all the numbers together, and all the variables

5x^2-2x-12=0

a = 5; b = -2; c = -12;
Δ = b2-4ac
Δ = -22-4·5·(-12)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{61}}{2*5}=\frac{2-2\sqrt{61}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{61}}{2*5}=\frac{2+2\sqrt{61}}{10}
$