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4x^2-7=233
We move all terms to the left:
4x^2-7-(233)=0
We add all the numbers together, and all the variables
4x^2-240=0
a = 4; b = 0; c = -240;
Δ = b2-4ac
Δ = 02-4·4·(-240)
Δ = 3840
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*4}=\frac{0-16\sqrt{15}}{8} =-\frac{16\sqrt{15}}{8} =-2\sqrt{15} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*4}=\frac{0+16\sqrt{15}}{8} =\frac{16\sqrt{15}}{8} =2\sqrt{15} $
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