1/4(12r)+7r-2(7)+9=40

Solution for 1/4(12r)+7r-2(7)+9=40 equation:

1/4(12r)+7r-2(7)+9=40

We move all terms to the left:

1/4(12r)+7r-2(7)+9-(40)=0


Domain of the equation: 412r!=0

r!=0/412

r!=0

r∈R


We add all the numbers together, and all the variables

7r+1/412r-58=0

We multiply all the terms by the denominator


7r*412r-58*412r+1=0

Wy multiply elements

2884r^2-23896r+1=0

a = 2884; b = -23896; c = +1;
Δ = b2-4ac
Δ = -238962-4·2884·1
Δ = 571007280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{571007280}=\sqrt{16*35687955}=\sqrt{16}*\sqrt{35687955}=4\sqrt{35687955}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23896)-4\sqrt{35687955}}{2*2884}=\frac{23896-4\sqrt{35687955}}{5768}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23896)+4\sqrt{35687955}}{2*2884}=\frac{23896+4\sqrt{35687955}}{5768}
$