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x+(5x-6)(5x-6)=20
We move all terms to the left:
x+(5x-6)(5x-6)-(20)=0
We multiply parentheses ..
(+25x^2-30x-30x+36)+x-20=0
We get rid of parentheses
25x^2-30x-30x+x+36-20=0
We add all the numbers together, and all the variables
25x^2-59x+16=0
a = 25; b = -59; c = +16;
Δ = b2-4ac
Δ = -592-4·25·16
Δ = 1881
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1881}=\sqrt{9*209}=\sqrt{9}*\sqrt{209}=3\sqrt{209}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-3\sqrt{209}}{2*25}=\frac{59-3\sqrt{209}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+3\sqrt{209}}{2*25}=\frac{59+3\sqrt{209}}{50} $
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