5/2q+2=6q+3+8q+4

Solution for 5/2q+2=6q+3+8q+4 equation:

5/2q+2=6q+3+8q+4

We move all terms to the left:

5/2q+2-(6q+3+8q+4)=0


Domain of the equation: 2q!=0

q!=0/2

q!=0

q∈R


We add all the numbers together, and all the variables

5/2q-(14q+7)+2=0

We get rid of parentheses

5/2q-14q-7+2=0

We multiply all the terms by the denominator


-14q*2q-7*2q+2*2q+5=0

Wy multiply elements

-28q^2-14q+4q+5=0

We add all the numbers together, and all the variables

-28q^2-10q+5=0

a = -28; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·(-28)·5
Δ = 660
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{165}}{2*-28}=\frac{10-2\sqrt{165}}{-56}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{165}}{2*-28}=\frac{10+2\sqrt{165}}{-56}
$