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(9x+7)(9x+7)=11
We move all terms to the left:
(9x+7)(9x+7)-(11)=0
We multiply parentheses ..
(+81x^2+63x+63x+49)-11=0
We get rid of parentheses
81x^2+63x+63x+49-11=0
We add all the numbers together, and all the variables
81x^2+126x+38=0
a = 81; b = 126; c = +38;
Δ = b2-4ac
Δ = 1262-4·81·38
Δ = 3564
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3564}=\sqrt{324*11}=\sqrt{324}*\sqrt{11}=18\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-18\sqrt{11}}{2*81}=\frac{-126-18\sqrt{11}}{162} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+18\sqrt{11}}{2*81}=\frac{-126+18\sqrt{11}}{162} $
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