4r-6/r-7=2

Solution for 4r-6/r-7=2 equation:

4r-6/r-7=2

We move all terms to the left:

4r-6/r-7-(2)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

4r-6/r-9=0

We multiply all the terms by the denominator


4r*r-9*r-6=0

We add all the numbers together, and all the variables

-9r+4r*r-6=0

Wy multiply elements

4r^2-9r-6=0

a = 4; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·4·(-6)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{177}}{2*4}=\frac{9-\sqrt{177}}{8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{177}}{2*4}=\frac{9+\sqrt{177}}{8}
$