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(5x-6)(9-x)=0
We add all the numbers together, and all the variables
(5x-6)(-1x+9)=0
We multiply parentheses ..
(-5x^2+45x+6x-54)=0
We get rid of parentheses
-5x^2+45x+6x-54=0
We add all the numbers together, and all the variables
-5x^2+51x-54=0
a = -5; b = 51; c = -54;
Δ = b2-4ac
Δ = 512-4·(-5)·(-54)
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-39}{2*-5}=\frac{-90}{-10} =+9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+39}{2*-5}=\frac{-12}{-10} =1+1/5 $
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