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6x(2x+7)+11=2x
We move all terms to the left:
6x(2x+7)+11-(2x)=0
We add all the numbers together, and all the variables
-2x+6x(2x+7)+11=0
We multiply parentheses
12x^2-2x+42x+11=0
We add all the numbers together, and all the variables
12x^2+40x+11=0
a = 12; b = 40; c = +11;
Δ = b2-4ac
Δ = 402-4·12·11
Δ = 1072
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{67}}{2*12}=\frac{-40-4\sqrt{67}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{67}}{2*12}=\frac{-40+4\sqrt{67}}{24} $
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