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45+10x-5x^2=0
a = -5; b = 10; c = +45;
Δ = b2-4ac
Δ = 102-4·(-5)·45
Δ = 1000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{10}}{2*-5}=\frac{-10-10\sqrt{10}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{10}}{2*-5}=\frac{-10+10\sqrt{10}}{-10} $
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