X=-5/2x-6

Solution for X=-5/2x-6 equation:

X=-5/2X-6

We move all terms to the left:

X-(-5/2X-6)=0


Domain of the equation: 2X-6)!=0

X∈R


We get rid of parentheses

X+5/2X+6=0

We multiply all the terms by the denominator


X*2X+6*2X+5=0

Wy multiply elements

2X^2+12X+5=0

a = 2; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·2·5
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{26}}{2*2}=\frac{-12-2\sqrt{26}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{26}}{2*2}=\frac{-12+2\sqrt{26}}{4}
$