(2x+5)(x-2)=55

Solution for (2x+5)(x-2)=55 equation:

(2x+5)(x-2)=55

We move all terms to the left:

(2x+5)(x-2)-(55)=0

We multiply parentheses ..

(+2x^2-4x+5x-10)-55=0

We get rid of parentheses

2x^2-4x+5x-10-55=0

We add all the numbers together, and all the variables

2x^2+x-65=0

a = 2; b = 1; c = -65;
Δ = b2-4ac
Δ = 12-4·2·(-65)
Δ = 521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{521}}{2*2}=\frac{-1-\sqrt{521}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{521}}{2*2}=\frac{-1+\sqrt{521}}{4}
$