12x+42=-17/2x-14

Solution for 12x+42=-17/2x-14 equation:

12x+42=-17/2x-14

We move all terms to the left:

12x+42-(-17/2x-14)=0


Domain of the equation: 2x-14)!=0

x∈R


We get rid of parentheses

12x+17/2x+14+42=0

We multiply all the terms by the denominator


12x*2x+14*2x+42*2x+17=0

Wy multiply elements

24x^2+28x+84x+17=0

We add all the numbers together, and all the variables

24x^2+112x+17=0

a = 24; b = 112; c = +17;
Δ = b2-4ac
Δ = 1122-4·24·17
Δ = 10912
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:

$\sqrt{\Delta}=\sqrt{10912}=\sqrt{16*682}=\sqrt{16}*\sqrt{682}=4\sqrt{682}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{682}}{2*24}=\frac{-112-4\sqrt{682}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{682}}{2*24}=\frac{-112+4\sqrt{682}}{48}
$