-4(x)=1/2x-14

Solution for -4(x)=1/2x-14 equation:

-4(x)=1/2x-14

We move all terms to the left:

-4(x)-(1/2x-14)=0


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

x∈R


We get rid of parentheses

-4x-1/2x+14=0

We multiply all the terms by the denominator


-4x*2x+14*2x-1=0

Wy multiply elements

-8x^2+28x-1=0

a = -8; b = 28; c = -1;
Δ = b2-4ac
Δ = 282-4·(-8)·(-1)
Δ = 752
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:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{47}}{2*-8}=\frac{-28-4\sqrt{47}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{47}}{2*-8}=\frac{-28+4\sqrt{47}}{-16}
$