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5x^2-30x-78=0
a = 5; b = -30; c = -78;
Δ = b2-4ac
Δ = -302-4·5·(-78)
Δ = 2460
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2460}=\sqrt{4*615}=\sqrt{4}*\sqrt{615}=2\sqrt{615}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{615}}{2*5}=\frac{30-2\sqrt{615}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{615}}{2*5}=\frac{30+2\sqrt{615}}{10} $
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