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4x(2x+1)=4x^2+48
We move all terms to the left:
4x(2x+1)-(4x^2+48)=0
We multiply parentheses
8x^2+4x-(4x^2+48)=0
We get rid of parentheses
8x^2-4x^2+4x-48=0
We add all the numbers together, and all the variables
4x^2+4x-48=0
a = 4; b = 4; c = -48;
Δ = b2-4ac
Δ = 42-4·4·(-48)
Δ = 784
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{784}=28$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-28}{2*4}=\frac{-32}{8} =-4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+28}{2*4}=\frac{24}{8} =3 $
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