1/2x+10/2=7x-7

Solution for 1/2x+10/2=7x-7 equation:

1/2x+10/2=7x-7

We move all terms to the left:

1/2x+10/2-(7x-7)=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-7)+5=0

We get rid of parentheses

1/2x-7x+7+5=0

We multiply all the terms by the denominator


-7x*2x+7*2x+5*2x+1=0

Wy multiply elements

-14x^2+14x+10x+1=0

We add all the numbers together, and all the variables

-14x^2+24x+1=0

a = -14; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-14)·1
Δ = 632
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:

$\sqrt{\Delta}=\sqrt{632}=\sqrt{4*158}=\sqrt{4}*\sqrt{158}=2\sqrt{158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{158}}{2*-14}=\frac{-24-2\sqrt{158}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{158}}{2*-14}=\frac{-24+2\sqrt{158}}{-28}
$