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10x^2+9=90
We move all terms to the left:
10x^2+9-(90)=0
We add all the numbers together, and all the variables
10x^2-81=0
a = 10; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·10·(-81)
Δ = 3240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3240}=\sqrt{324*10}=\sqrt{324}*\sqrt{10}=18\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{10}}{2*10}=\frac{0-18\sqrt{10}}{20} =-\frac{18\sqrt{10}}{20} =-\frac{9\sqrt{10}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{10}}{2*10}=\frac{0+18\sqrt{10}}{20} =\frac{18\sqrt{10}}{20} =\frac{9\sqrt{10}}{10} $
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