(1/4)(9+x)=6

Solution for (1/4)(9+x)=6 equation:

(1/4)(9+x)=6

We move all terms to the left:

(1/4)(9+x)-(6)=0


Domain of the equation: 4)(9+x)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(x+9)-6=0

We multiply parentheses ..

(+x^2+1/4*9)-6=0

We multiply all the terms by the denominator


(+x^2+1-6*4*9)=0

We get rid of parentheses

x^2+1-6*4*9=0

We add all the numbers together, and all the variables

x^2-215=0

a = 1; b = 0; c = -215;
Δ = b2-4ac
Δ = 02-4·1·(-215)
Δ = 860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{860}=\sqrt{4*215}=\sqrt{4}*\sqrt{215}=2\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{215}}{2*1}=\frac{0-2\sqrt{215}}{2}
=-\frac{2\sqrt{215}}{2}
=-\sqrt{215}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{215}}{2*1}=\frac{0+2\sqrt{215}}{2}
=\frac{2\sqrt{215}}{2}
=\sqrt{215}
$