1/2x-1.5=7x-7+3

Solution for 1/2x-1.5=7x-7+3 equation:

1/2x-1.5=7x-7+3

We move all terms to the left:

1/2x-1.5-(7x-7+3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(7x-4)-1.5=0

We get rid of parentheses

1/2x-7x+4-1.5=0

We multiply all the terms by the denominator


-7x*2x+4*2x-(1.5)*2x+1=0

We multiply parentheses

-7x*2x+4*2x-3x+1=0

Wy multiply elements

-14x^2+8x-3x+1=0

We add all the numbers together, and all the variables

-14x^2+5x+1=0

a = -14; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-14)·1
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*-14}=\frac{-14}{-28}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*-14}=\frac{4}{-28}
=-1/7
$