2x(x-5)=9x+25

Solution for 2x(x-5)=9x+25 equation:

2x(x-5)=9x+25

We move all terms to the left:

2x(x-5)-(9x+25)=0

We multiply parentheses

2x^2-10x-(9x+25)=0

We get rid of parentheses

2x^2-10x-9x-25=0

We add all the numbers together, and all the variables

2x^2-19x-25=0

a = 2; b = -19; c = -25;
Δ = b2-4ac
Δ = -192-4·2·(-25)
Δ = 561
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{-(-19)-\sqrt{561}}{2*2}=\frac{19-\sqrt{561}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{561}}{2*2}=\frac{19+\sqrt{561}}{4}
$