5x^2-2x-53=-2

Solution for 5x^2-2x-53=-2 equation:

5x^2-2x-53=-2

We move all terms to the left:

5x^2-2x-53-(-2)=0

We add all the numbers together, and all the variables

5x^2-2x-51=0

a = 5; b = -2; c = -51;
Δ = b2-4ac
Δ = -22-4·5·(-51)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-32}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+32}{2*5}=\frac{34}{10}
=3+2/5
$