12(x)=3/2x+14

Solution for 12(x)=3/2x+14 equation:

12(x)=3/2x+14

We move all terms to the left:

12(x)-(3/2x+14)=0


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

x∈R


We get rid of parentheses

12x-3/2x-14=0

We multiply all the terms by the denominator


12x*2x-14*2x-3=0

Wy multiply elements

24x^2-28x-3=0

a = 24; b = -28; c = -3;
Δ = b2-4ac
Δ = -282-4·24·(-3)
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{67}}{2*24}=\frac{28-4\sqrt{67}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{67}}{2*24}=\frac{28+4\sqrt{67}}{48}
$