x(x-3)=2x^2+5x+7

Solution for x(x-3)=2x^2+5x+7 equation:

x(x-3)=2x^2+5x+7

We move all terms to the left:

x(x-3)-(2x^2+5x+7)=0

We multiply parentheses

x^2-3x-(2x^2+5x+7)=0

We get rid of parentheses

x^2-2x^2-3x-5x-7=0

We add all the numbers together, and all the variables

-1x^2-8x-7=0

a = -1; b = -8; c = -7;
Δ = b2-4ac
Δ = -82-4·(-1)·(-7)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6}{2*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6}{2*-1}=\frac{14}{-2}
=-7
$