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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x(-1x+7)-(3(x+2))=0

We multiply parentheses

-2x^2+14x-(3(x+2))=0


We calculate terms in parentheses: -(3(x+2)), so:

3(x+2)

We multiply parentheses

3x+6

Back to the equation:

-(3x+6)


We get rid of parentheses

-2x^2+14x-3x-6=0

We add all the numbers together, and all the variables

-2x^2+11x-6=0

a = -2; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·(-2)·(-6)
Δ = 73
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{-(11)-\sqrt{73}}{2*-2}=\frac{-11-\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{73}}{2*-2}=\frac{-11+\sqrt{73}}{-4}
$