4q+5q=6/7q

Solution for 4q+5q=6/7q equation:

4q+5q=6/7q

We move all terms to the left:

4q+5q-(6/7q)=0


Domain of the equation: 7q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

4q+5q-(+6/7q)=0

We add all the numbers together, and all the variables

9q-(+6/7q)=0

We get rid of parentheses

9q-6/7q=0

We multiply all the terms by the denominator


9q*7q-6=0

Wy multiply elements

63q^2-6=0

a = 63; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·63·(-6)
Δ = 1512
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:

$\sqrt{\Delta}=\sqrt{1512}=\sqrt{36*42}=\sqrt{36}*\sqrt{42}=6\sqrt{42}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{42}}{2*63}=\frac{0-6\sqrt{42}}{126}
=-\frac{6\sqrt{42}}{126}
=-\frac{\sqrt{42}}{21}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{42}}{2*63}=\frac{0+6\sqrt{42}}{126}
=\frac{6\sqrt{42}}{126}
=\frac{\sqrt{42}}{21}
$