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6x^2-130x+60=0
a = 6; b = -130; c = +60;
Δ = b2-4ac
Δ = -1302-4·6·60
Δ = 15460
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{15460}=\sqrt{4*3865}=\sqrt{4}*\sqrt{3865}=2\sqrt{3865}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{3865}}{2*6}=\frac{130-2\sqrt{3865}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{3865}}{2*6}=\frac{130+2\sqrt{3865}}{12} $
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