x^2+10x-162.5=0

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Solution for x^2+10x-162.5=0 equation:



x^2+10x-162.5=0
a = 1; b = 10; c = -162.5;
Δ = b2-4ac
Δ = 102-4·1·(-162.5)
Δ = 750
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:
$\sqrt{\Delta}=\sqrt{750}=\sqrt{25*30}=\sqrt{25}*\sqrt{30}=5\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-5\sqrt{30}}{2*1}=\frac{-10-5\sqrt{30}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+5\sqrt{30}}{2*1}=\frac{-10+5\sqrt{30}}{2} $

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