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(3x-5)(3x-5)=20
We move all terms to the left:
(3x-5)(3x-5)-(20)=0
We multiply parentheses ..
(+9x^2-15x-15x+25)-20=0
We get rid of parentheses
9x^2-15x-15x+25-20=0
We add all the numbers together, and all the variables
9x^2-30x+5=0
a = 9; b = -30; c = +5;
Δ = b2-4ac
Δ = -302-4·9·5
Δ = 720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-12\sqrt{5}}{2*9}=\frac{30-12\sqrt{5}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+12\sqrt{5}}{2*9}=\frac{30+12\sqrt{5}}{18} $
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