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10x^2-3=17
We move all terms to the left:
10x^2-3-(17)=0
We add all the numbers together, and all the variables
10x^2-20=0
a = 10; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·10·(-20)
Δ = 800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*10}=\frac{0-20\sqrt{2}}{20} =-\frac{20\sqrt{2}}{20} =-\sqrt{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*10}=\frac{0+20\sqrt{2}}{20} =\frac{20\sqrt{2}}{20} =\sqrt{2} $
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