x(x-4)=x(2x+5)+10

Solution for x(x-4)=x(2x+5)+10 equation:

x(x-4)=x(2x+5)+10

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(x(2x+5)+10), so:

x(2x+5)+10

We multiply parentheses

2x^2+5x+10

Back to the equation:

-(2x^2+5x+10)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-9x-10=0

a = -1; b = -9; c = -10;
Δ = b2-4ac
Δ = -92-4·(-1)·(-10)
Δ = 41
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{-(-9)-\sqrt{41}}{2*-1}=\frac{9-\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{41}}{2*-1}=\frac{9+\sqrt{41}}{-2}
$