(x+5)(2x-4)=5

Solution for (x+5)(2x-4)=5 equation:

(x+5)(2x-4)=5

We move all terms to the left:

(x+5)(2x-4)-(5)=0

We multiply parentheses ..

(+2x^2-4x+10x-20)-5=0

We get rid of parentheses

2x^2-4x+10x-20-5=0

We add all the numbers together, and all the variables

2x^2+6x-25=0

a = 2; b = 6; c = -25;
Δ = b2-4ac
Δ = 62-4·2·(-25)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{59}}{2*2}=\frac{-6-2\sqrt{59}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{59}}{2*2}=\frac{-6+2\sqrt{59}}{4}
$