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15x(x-9)-5(9-x)=9=0
We move all terms to the left:
15x(x-9)-5(9-x)-(9)=0
We add all the numbers together, and all the variables
15x(x-9)-5(-1x+9)-9=0
We multiply parentheses
15x^2-135x+5x-45-9=0
We add all the numbers together, and all the variables
15x^2-130x-54=0
a = 15; b = -130; c = -54;
Δ = b2-4ac
Δ = -1302-4·15·(-54)
Δ = 20140
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20140}=\sqrt{4*5035}=\sqrt{4}*\sqrt{5035}=2\sqrt{5035}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{5035}}{2*15}=\frac{130-2\sqrt{5035}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{5035}}{2*15}=\frac{130+2\sqrt{5035}}{30} $
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