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7x(4x+1)=476
We move all terms to the left:
7x(4x+1)-(476)=0
We multiply parentheses
28x^2+7x-476=0
a = 28; b = 7; c = -476;
Δ = b2-4ac
Δ = 72-4·28·(-476)
Δ = 53361
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{53361}=231$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-231}{2*28}=\frac{-238}{56} =-4+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+231}{2*28}=\frac{224}{56} =4 $
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