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x2-7x-9.75=0
We add all the numbers together, and all the variables
x^2-7x-9.75=0
a = 1; b = -7; c = -9.75;
Δ = b2-4ac
Δ = -72-4·1·(-9.75)
Δ = 88
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-2\sqrt{22}}{2*1}=\frac{7-2\sqrt{22}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+2\sqrt{22}}{2*1}=\frac{7+2\sqrt{22}}{2} $
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