q/8+q2=20/5

Solution for q/8+q2=20/5 equation:

q/8+q2=20/5

We move all terms to the left:

q/8+q2-(20/5)=0

We add all the numbers together, and all the variables

q/8+q2-4=0

We add all the numbers together, and all the variables

q^2+q/8-4=0

We multiply all the terms by the denominator


q^2*8+q-4*8=0

We add all the numbers together, and all the variables

q^2*8+q-32=0

Wy multiply elements

8q^2+q-32=0

a = 8; b = 1; c = -32;
Δ = b2-4ac
Δ = 12-4·8·(-32)
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{41}}{2*8}=\frac{-1-5\sqrt{41}}{16}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{41}}{2*8}=\frac{-1+5\sqrt{41}}{16}
$