5x^2-8x-30=x^2-2x-4

Solution for 5x^2-8x-30=x^2-2x-4 equation:

5x^2-8x-30=x^2-2x-4

We move all terms to the left:

5x^2-8x-30-(x^2-2x-4)=0

We get rid of parentheses

5x^2-x^2-8x+2x+4-30=0

We add all the numbers together, and all the variables

4x^2-6x-26=0

a = 4; b = -6; c = -26;
Δ = b2-4ac
Δ = -62-4·4·(-26)
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{113}}{2*4}=\frac{6-2\sqrt{113}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{113}}{2*4}=\frac{6+2\sqrt{113}}{8}
$