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5x^2+11=90
We move all terms to the left:
5x^2+11-(90)=0
We add all the numbers together, and all the variables
5x^2-79=0
a = 5; b = 0; c = -79;
Δ = b2-4ac
Δ = 02-4·5·(-79)
Δ = 1580
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1580}=\sqrt{4*395}=\sqrt{4}*\sqrt{395}=2\sqrt{395}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{395}}{2*5}=\frac{0-2\sqrt{395}}{10} =-\frac{2\sqrt{395}}{10} =-\frac{\sqrt{395}}{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{395}}{2*5}=\frac{0+2\sqrt{395}}{10} =\frac{2\sqrt{395}}{10} =\frac{\sqrt{395}}{5} $
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