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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(2(x+7)), so:

2(x+7)

We multiply parentheses

2x+14

Back to the equation:

-(2x+14)


We get rid of parentheses

x^2-3x-2x-14=0

We add all the numbers together, and all the variables

x^2-5x-14=0

a = 1; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·1·(-14)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*1}=\frac{14}{2}
=7
$