-8x-1/2x=15

Solution for -8x-1/2x=15 equation:

-8x-1/2x=15

We move all terms to the left:

-8x-1/2x-(15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


-8x*2x-15*2x-1=0

Wy multiply elements

-16x^2-30x-1=0

a = -16; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·(-16)·(-1)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{209}}{2*-16}=\frac{30-2\sqrt{209}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{209}}{2*-16}=\frac{30+2\sqrt{209}}{-32}
$