1/2x-10=65+8x

Solution for 1/2x-10=65+8x equation:

1/2x-10=65+8x

We move all terms to the left:

1/2x-10-(65+8x)=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-(8x+65)-10=0

We get rid of parentheses

1/2x-8x-65-10=0

We multiply all the terms by the denominator


-8x*2x-65*2x-10*2x+1=0

Wy multiply elements

-16x^2-130x-20x+1=0

We add all the numbers together, and all the variables

-16x^2-150x+1=0

a = -16; b = -150; c = +1;
Δ = b2-4ac
Δ = -1502-4·(-16)·1
Δ = 22564
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:

$\sqrt{\Delta}=\sqrt{22564}=\sqrt{4*5641}=\sqrt{4}*\sqrt{5641}=2\sqrt{5641}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5641}}{2*-16}=\frac{150-2\sqrt{5641}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5641}}{2*-16}=\frac{150+2\sqrt{5641}}{-32}
$