(1/5)(5x+12)=18

Solution for (1/5)(5x+12)=18 equation:

(1/5)(5x+12)=18

We move all terms to the left:

(1/5)(5x+12)-(18)=0


Domain of the equation: 5)(5x+12)!=0

x∈R


We add all the numbers together, and all the variables

(+1/5)(5x+12)-18=0

We multiply parentheses ..

(+5x^2+1/5*12)-18=0

We multiply all the terms by the denominator


(+5x^2+1-18*5*12)=0

We get rid of parentheses

5x^2+1-18*5*12=0

We add all the numbers together, and all the variables

5x^2-1079=0

a = 5; b = 0; c = -1079;
Δ = b2-4ac
Δ = 02-4·5·(-1079)
Δ = 21580
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:

$\sqrt{\Delta}=\sqrt{21580}=\sqrt{4*5395}=\sqrt{4}*\sqrt{5395}=2\sqrt{5395}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5395}}{2*5}=\frac{0-2\sqrt{5395}}{10}
=-\frac{2\sqrt{5395}}{10}
=-\frac{\sqrt{5395}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5395}}{2*5}=\frac{0+2\sqrt{5395}}{10}
=\frac{2\sqrt{5395}}{10}
=\frac{\sqrt{5395}}{5}
$