3*(1/4*9x+5)=18+x

Solution for 3*(1/4*9x+5)=18+x equation:

3(1/4*9x+5)=18+x

We move all terms to the left:

3(1/4*9x+5)-(18+x)=0


Domain of the equation: 4*9x+5)!=0

x∈R


We add all the numbers together, and all the variables

3(1/4*9x+5)-(x+18)=0

We multiply parentheses

27x^2-(x+18)+15=0

We get rid of parentheses

27x^2-x-18+15=0

We add all the numbers together, and all the variables

27x^2-1x-3=0

a = 27; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·27·(-3)
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{13}}{2*27}=\frac{1-5\sqrt{13}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{13}}{2*27}=\frac{1+5\sqrt{13}}{54}
$