2(x+5)(x-2)=x(x+5)+220

Solution for 2(x+5)(x-2)=x(x+5)+220 equation:

2(x+5)(x-2)=x(x+5)+220

We move all terms to the left:

2(x+5)(x-2)-(x(x+5)+220)=0

We multiply parentheses ..

2(+x^2-2x+5x-10)-(x(x+5)+220)=0


We calculate terms in parentheses: -(x(x+5)+220), so:

x(x+5)+220

We multiply parentheses

x^2+5x+220

Back to the equation:

-(x^2+5x+220)


We multiply parentheses

2x^2-4x+10x-(x^2+5x+220)-20=0

We get rid of parentheses

2x^2-x^2-4x+10x-5x-220-20=0

We add all the numbers together, and all the variables

x^2+x-240=0

a = 1; b = 1; c = -240;
Δ = b2-4ac
Δ = 12-4·1·(-240)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-31}{2*1}=\frac{-32}{2}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+31}{2*1}=\frac{30}{2}
=15
$