9+1/2x=8x+7

Solution for 9+1/2x=8x+7 equation:

9+1/2x=8x+7

We move all terms to the left:

9+1/2x-(8x+7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-8x-7+9=0

We multiply all the terms by the denominator


-8x*2x-7*2x+9*2x+1=0

Wy multiply elements

-16x^2-14x+18x+1=0

We add all the numbers together, and all the variables

-16x^2+4x+1=0

a = -16; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-16)·1
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{5}}{2*-16}=\frac{-4-4\sqrt{5}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{5}}{2*-16}=\frac{-4+4\sqrt{5}}{-32}
$