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4x(2x+7)=+11
We move all terms to the left:
4x(2x+7)-(+11)=0
We add all the numbers together, and all the variables
4x(2x+7)-11=0
We multiply parentheses
8x^2+28x-11=0
a = 8; b = 28; c = -11;
Δ = b2-4ac
Δ = 282-4·8·(-11)
Δ = 1136
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{71}}{2*8}=\frac{-28-4\sqrt{71}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{71}}{2*8}=\frac{-28+4\sqrt{71}}{16} $
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