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5x^2-100=160
We move all terms to the left:
5x^2-100-(160)=0
We add all the numbers together, and all the variables
5x^2-260=0
a = 5; b = 0; c = -260;
Δ = b2-4ac
Δ = 02-4·5·(-260)
Δ = 5200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{13}}{2*5}=\frac{0-20\sqrt{13}}{10} =-\frac{20\sqrt{13}}{10} =-2\sqrt{13} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{13}}{2*5}=\frac{0+20\sqrt{13}}{10} =\frac{20\sqrt{13}}{10} =2\sqrt{13} $
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