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X2+3X^2=43
We move all terms to the left:
X2+3X^2-(43)=0
We add all the numbers together, and all the variables
4X^2-43=0
a = 4; b = 0; c = -43;
Δ = b2-4ac
Δ = 02-4·4·(-43)
Δ = 688
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{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{43}}{2*4}=\frac{0-4\sqrt{43}}{8} =-\frac{4\sqrt{43}}{8} =-\frac{\sqrt{43}}{2}X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{43}}{2*4}=\frac{0+4\sqrt{43}}{8} =\frac{4\sqrt{43}}{8} =\frac{\sqrt{43}}{2}
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