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5x^2-14=20
We move all terms to the left:
5x^2-14-(20)=0
We add all the numbers together, and all the variables
5x^2-34=0
a = 5; b = 0; c = -34;
Δ = b2-4ac
Δ = 02-4·5·(-34)
Δ = 680
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{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{170}}{2*5}=\frac{0-2\sqrt{170}}{10} =-\frac{2\sqrt{170}}{10} =-\frac{\sqrt{170}}{5}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{170}}{2*5}=\frac{0+2\sqrt{170}}{10} =\frac{2\sqrt{170}}{10} =\frac{\sqrt{170}}{5}
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