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4x(x+)=224
We move all terms to the left:
4x(x+)-(224)=0
We add all the numbers together, and all the variables
4x(+x)-224=0
We multiply parentheses
4x^2-224=0
a = 4; b = 0; c = -224;
Δ = b2-4ac
Δ = 02-4·4·(-224)
Δ = 3584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{14}}{2*4}=\frac{0-16\sqrt{14}}{8} =-\frac{16\sqrt{14}}{8} =-2\sqrt{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{14}}{2*4}=\frac{0+16\sqrt{14}}{8} =\frac{16\sqrt{14}}{8} =2\sqrt{14} $
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