18x+270+18x=x^2+15x

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Solution for 18x+270+18x=x^2+15x equation:



18x+270+18x=x^2+15x
We move all terms to the left:
18x+270+18x-(x^2+15x)=0
We add all the numbers together, and all the variables
36x-(x^2+15x)+270=0
We get rid of parentheses
-x^2+36x-15x+270=0
We add all the numbers together, and all the variables
-1x^2+21x+270=0
a = -1; b = 21; c = +270;
Δ = b2-4ac
Δ = 212-4·(-1)·270
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-39}{2*-1}=\frac{-60}{-2} =+30 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+39}{2*-1}=\frac{18}{-2} =-9 $

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