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7x^2-92x+225=0
a = 7; b = -92; c = +225;
Δ = b2-4ac
Δ = -922-4·7·225
Δ = 2164
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2164}=\sqrt{4*541}=\sqrt{4}*\sqrt{541}=2\sqrt{541}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-2\sqrt{541}}{2*7}=\frac{92-2\sqrt{541}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+2\sqrt{541}}{2*7}=\frac{92+2\sqrt{541}}{14} $
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