5q+14=5/8q

Solution for 5q+14=5/8q equation:

5q+14=5/8q

We move all terms to the left:

5q+14-(5/8q)=0


Domain of the equation: 8q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

5q-(+5/8q)+14=0

We get rid of parentheses

5q-5/8q+14=0

We multiply all the terms by the denominator


5q*8q+14*8q-5=0

Wy multiply elements

40q^2+112q-5=0

a = 40; b = 112; c = -5;
Δ = b2-4ac
Δ = 1122-4·40·(-5)
Δ = 13344
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:

$\sqrt{\Delta}=\sqrt{13344}=\sqrt{16*834}=\sqrt{16}*\sqrt{834}=4\sqrt{834}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{834}}{2*40}=\frac{-112-4\sqrt{834}}{80}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{834}}{2*40}=\frac{-112+4\sqrt{834}}{80}
$