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-5x^2+5x+7.5=0
a = -5; b = 5; c = +7.5;
Δ = b2-4ac
Δ = 52-4·(-5)·7.5
Δ = 175
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{175}=\sqrt{25*7}=\sqrt{25}*\sqrt{7}=5\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{7}}{2*-5}=\frac{-5-5\sqrt{7}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{7}}{2*-5}=\frac{-5+5\sqrt{7}}{-10} $
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