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5x^2+7=25
We move all terms to the left:
5x^2+7-(25)=0
We add all the numbers together, and all the variables
5x^2-18=0
a = 5; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·5·(-18)
Δ = 360
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*5}=\frac{0-6\sqrt{10}}{10} =-\frac{6\sqrt{10}}{10} =-\frac{3\sqrt{10}}{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*5}=\frac{0+6\sqrt{10}}{10} =\frac{6\sqrt{10}}{10} =\frac{3\sqrt{10}}{5} $
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