x=-90/2x-16

Solution for x=-90/2x-16 equation:

x=-90/2x-16

We move all terms to the left:

x-(-90/2x-16)=0


Domain of the equation: 2x-16)!=0

x∈R


We get rid of parentheses

x+90/2x+16=0

We multiply all the terms by the denominator


x*2x+16*2x+90=0

Wy multiply elements

2x^2+32x+90=0

a = 2; b = 32; c = +90;
Δ = b2-4ac
Δ = 322-4·2·90
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{19}}{2*2}=\frac{-32-4\sqrt{19}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{19}}{2*2}=\frac{-32+4\sqrt{19}}{4}
$