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(6x+7)(6x+7)=7
We move all terms to the left:
(6x+7)(6x+7)-(7)=0
We multiply parentheses ..
(+36x^2+42x+42x+49)-7=0
We get rid of parentheses
36x^2+42x+42x+49-7=0
We add all the numbers together, and all the variables
36x^2+84x+42=0
a = 36; b = 84; c = +42;
Δ = b2-4ac
Δ = 842-4·36·42
Δ = 1008
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-12\sqrt{7}}{2*36}=\frac{-84-12\sqrt{7}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+12\sqrt{7}}{2*36}=\frac{-84+12\sqrt{7}}{72} $
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