12x2+18x=x+5

Solution for 12x2+18x=x+5 equation:

12x^2+18x=x+5

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2+17x-5=0

a = 12; b = 17; c = -5;
Δ = b2-4ac
Δ = 172-4·12·(-5)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-23}{2*12}=\frac{-40}{24}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+23}{2*12}=\frac{6}{24}
=1/4
$