7x+12=2(x2+6)

Solution for 7x+12=2(x2+6) equation:

7x+12=2(x2+6)

We move all terms to the left:

7x+12-(2(x2+6))=0

We add all the numbers together, and all the variables

-(2(+x^2+6))+7x+12=0


We calculate terms in parentheses: -(2(+x^2+6)), so:

2(+x^2+6)

We multiply parentheses

2x^2+12

Back to the equation:

-(2x^2+12)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x^2+7x-12+12=0

We add all the numbers together, and all the variables

-2x^2+7x=0

a = -2; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-2)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-2}=\frac{0}{-4}
=0
$