1/2x+1=7x-15

Solution for 1/2x+1=7x-15 equation:

1/2x+1=7x-15

We move all terms to the left:

1/2x+1-(7x-15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-7x+15+1=0

We multiply all the terms by the denominator


-7x*2x+15*2x+1*2x+1=0

Wy multiply elements

-14x^2+30x+2x+1=0

We add all the numbers together, and all the variables

-14x^2+32x+1=0

a = -14; b = 32; c = +1;
Δ = b2-4ac
Δ = 322-4·(-14)·1
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-6\sqrt{30}}{2*-14}=\frac{-32-6\sqrt{30}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+6\sqrt{30}}{2*-14}=\frac{-32+6\sqrt{30}}{-28}
$