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-10x^2-6x+5=0
a = -10; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·(-10)·5
Δ = 236
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{59}}{2*-10}=\frac{6-2\sqrt{59}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{59}}{2*-10}=\frac{6+2\sqrt{59}}{-20} $
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