7x(x+2)=3(x+12)-2

Solution for 7x(x+2)=3(x+12)-2 equation:

7x(x+2)=3(x+12)-2

We move all terms to the left:

7x(x+2)-(3(x+12)-2)=0

We multiply parentheses

7x^2+14x-(3(x+12)-2)=0


We calculate terms in parentheses: -(3(x+12)-2), so:

3(x+12)-2

We multiply parentheses

3x+36-2

We add all the numbers together, and all the variables

3x+34

Back to the equation:

-(3x+34)


We get rid of parentheses

7x^2+14x-3x-34=0

We add all the numbers together, and all the variables

7x^2+11x-34=0

a = 7; b = 11; c = -34;
Δ = b2-4ac
Δ = 112-4·7·(-34)
Δ = 1073
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{1073}}{2*7}=\frac{-11-\sqrt{1073}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{1073}}{2*7}=\frac{-11+\sqrt{1073}}{14}
$