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(9x-1)(9x-1)+24x+14=180
We move all terms to the left:
(9x-1)(9x-1)+24x+14-(180)=0
We add all the numbers together, and all the variables
24x+(9x-1)(9x-1)-166=0
We multiply parentheses ..
(+81x^2-9x-9x+1)+24x-166=0
We get rid of parentheses
81x^2-9x-9x+24x+1-166=0
We add all the numbers together, and all the variables
81x^2+6x-165=0
a = 81; b = 6; c = -165;
Δ = b2-4ac
Δ = 62-4·81·(-165)
Δ = 53496
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{53496}=\sqrt{36*1486}=\sqrt{36}*\sqrt{1486}=6\sqrt{1486}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{1486}}{2*81}=\frac{-6-6\sqrt{1486}}{162} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{1486}}{2*81}=\frac{-6+6\sqrt{1486}}{162} $
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