-1/2x+5=-4x+12

Solution for -1/2x+5=-4x+12 equation:

-1/2x+5=-4x+12

We move all terms to the left:

-1/2x+5-(-4x+12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x+4x-12+5=0

We multiply all the terms by the denominator


4x*2x-12*2x+5*2x-1=0

Wy multiply elements

8x^2-24x+10x-1=0

We add all the numbers together, and all the variables

8x^2-14x-1=0

a = 8; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·8·(-1)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{57}}{2*8}=\frac{14-2\sqrt{57}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{57}}{2*8}=\frac{14+2\sqrt{57}}{16}
$