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(9x-5)(5x-5)=x
We move all terms to the left:
(9x-5)(5x-5)-(x)=0
We add all the numbers together, and all the variables
-1x+(9x-5)(5x-5)=0
We multiply parentheses ..
(+45x^2-45x-25x+25)-1x=0
We get rid of parentheses
45x^2-45x-25x-1x+25=0
We add all the numbers together, and all the variables
45x^2-71x+25=0
a = 45; b = -71; c = +25;
Δ = b2-4ac
Δ = -712-4·45·25
Δ = 541
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-\sqrt{541}}{2*45}=\frac{71-\sqrt{541}}{90} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+\sqrt{541}}{2*45}=\frac{71+\sqrt{541}}{90} $
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