1/4q-2=q+.7

Solution for 1/4q-2=q+.7 equation:

1/4q-2=q+.7

We move all terms to the left:

1/4q-2-(q+.7)=0


Domain of the equation: 4q!=0

q!=0/4

q!=0

q∈R


We add all the numbers together, and all the variables

1/4q-(q+0.7)-2=0

We get rid of parentheses

1/4q-q-0.7-2=0

We multiply all the terms by the denominator


-q*4q-(0.7)*4q-2*4q+1=0

We multiply parentheses

-q*4q-2.8q-2*4q+1=0

Wy multiply elements

-4q^2-2.8q-8q+1=0

We add all the numbers together, and all the variables

-4q^2-10.8q+1=0

a = -4; b = -10.8; c = +1;
Δ = b2-4ac
Δ = -10.82-4·(-4)·1
Δ = 132.64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10.8)-\sqrt{132.64}}{2*-4}=\frac{10.8-\sqrt{132.64}}{-8}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10.8)+\sqrt{132.64}}{2*-4}=\frac{10.8+\sqrt{132.64}}{-8}
$