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4x(2x+6)=7
We move all terms to the left:
4x(2x+6)-(7)=0
We multiply parentheses
8x^2+24x-7=0
a = 8; b = 24; c = -7;
Δ = b2-4ac
Δ = 242-4·8·(-7)
Δ = 800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-20\sqrt{2}}{2*8}=\frac{-24-20\sqrt{2}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+20\sqrt{2}}{2*8}=\frac{-24+20\sqrt{2}}{16} $
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