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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-143=0

a = 1; b = 0; c = -143;
Δ = b2-4ac
Δ = 02-4·1·(-143)
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{143}}{2*1}=\frac{0-2\sqrt{143}}{2}
=-\frac{2\sqrt{143}}{2}
=-\sqrt{143}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{143}}{2*1}=\frac{0+2\sqrt{143}}{2}
=\frac{2\sqrt{143}}{2}
=\sqrt{143}
$