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(3x-4)(3x-5)=25
We move all terms to the left:
(3x-4)(3x-5)-(25)=0
We multiply parentheses ..
(+9x^2-15x-12x+20)-25=0
We get rid of parentheses
9x^2-15x-12x+20-25=0
We add all the numbers together, and all the variables
9x^2-27x-5=0
a = 9; b = -27; c = -5;
Δ = b2-4ac
Δ = -272-4·9·(-5)
Δ = 909
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{909}=\sqrt{9*101}=\sqrt{9}*\sqrt{101}=3\sqrt{101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{101}}{2*9}=\frac{27-3\sqrt{101}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{101}}{2*9}=\frac{27+3\sqrt{101}}{18} $
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