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(5x+3)(3x-9)=x
We move all terms to the left:
(5x+3)(3x-9)-(x)=0
We add all the numbers together, and all the variables
-1x+(5x+3)(3x-9)=0
We multiply parentheses ..
(+15x^2-45x+9x-27)-1x=0
We get rid of parentheses
15x^2-45x+9x-1x-27=0
We add all the numbers together, and all the variables
15x^2-37x-27=0
a = 15; b = -37; c = -27;
Δ = b2-4ac
Δ = -372-4·15·(-27)
Δ = 2989
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2989}=\sqrt{49*61}=\sqrt{49}*\sqrt{61}=7\sqrt{61}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-7\sqrt{61}}{2*15}=\frac{37-7\sqrt{61}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+7\sqrt{61}}{2*15}=\frac{37+7\sqrt{61}}{30} $
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