14=(-1/2)(8x+12)

Solution for 14=(-1/2)(8x+12) equation:

14=(-1/2)(8x+12)

We move all terms to the left:

14-((-1/2)(8x+12))=0


Domain of the equation: 2)(8x+12))!=0

x∈R


We multiply parentheses ..

-((-8x^2-1/2*12))+14=0

We multiply all the terms by the denominator


-((-8x^2-1+14*2*12))=0


We calculate terms in parentheses: -((-8x^2-1+14*2*12)), so:

(-8x^2-1+14*2*12)

We get rid of parentheses

-8x^2-1+14*2*12

We add all the numbers together, and all the variables

-8x^2+335

Back to the equation:

-(-8x^2+335)


We get rid of parentheses

8x^2-335=0

a = 8; b = 0; c = -335;
Δ = b2-4ac
Δ = 02-4·8·(-335)
Δ = 10720
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10720}=\sqrt{16*670}=\sqrt{16}*\sqrt{670}=4\sqrt{670}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{670}}{2*8}=\frac{0-4\sqrt{670}}{16}
=-\frac{4\sqrt{670}}{16}
=-\frac{\sqrt{670}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{670}}{2*8}=\frac{0+4\sqrt{670}}{16}
=\frac{4\sqrt{670}}{16}
=\frac{\sqrt{670}}{4}
$