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25(x-15)(x-15)-27=106
We move all terms to the left:
25(x-15)(x-15)-27-(106)=0
We add all the numbers together, and all the variables
25(x-15)(x-15)-133=0
We multiply parentheses ..
25(+x^2-15x-15x+225)-133=0
We multiply parentheses
25x^2-375x-375x+5625-133=0
We add all the numbers together, and all the variables
25x^2-750x+5492=0
a = 25; b = -750; c = +5492;
Δ = b2-4ac
Δ = -7502-4·25·5492
Δ = 13300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13300}=\sqrt{100*133}=\sqrt{100}*\sqrt{133}=10\sqrt{133}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-750)-10\sqrt{133}}{2*25}=\frac{750-10\sqrt{133}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-750)+10\sqrt{133}}{2*25}=\frac{750+10\sqrt{133}}{50} $
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