5/2x+7=-8x-6

Solution for 5/2x+7=-8x-6 equation:

5/2x+7=-8x-6

We move all terms to the left:

5/2x+7-(-8x-6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x+8x+6+7=0

We multiply all the terms by the denominator


8x*2x+6*2x+7*2x+5=0

Wy multiply elements

16x^2+12x+14x+5=0

We add all the numbers together, and all the variables

16x^2+26x+5=0

a = 16; b = 26; c = +5;
Δ = b2-4ac
Δ = 262-4·16·5
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{89}}{2*16}=\frac{-26-2\sqrt{89}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{89}}{2*16}=\frac{-26+2\sqrt{89}}{32}
$