(2x-10)(x+6)=5

Solution for (2x-10)(x+6)=5 equation:

(2x-10)(x+6)=5

We move all terms to the left:

(2x-10)(x+6)-(5)=0

We multiply parentheses ..

(+2x^2+12x-10x-60)-5=0

We get rid of parentheses

2x^2+12x-10x-60-5=0

We add all the numbers together, and all the variables

2x^2+2x-65=0

a = 2; b = 2; c = -65;
Δ = b2-4ac
Δ = 22-4·2·(-65)
Δ = 524
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:

$\sqrt{\Delta}=\sqrt{524}=\sqrt{4*131}=\sqrt{4}*\sqrt{131}=2\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{131}}{2*2}=\frac{-2-2\sqrt{131}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{131}}{2*2}=\frac{-2+2\sqrt{131}}{4}
$