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4x^2+84x-178=0
a = 4; b = 84; c = -178;
Δ = b2-4ac
Δ = 842-4·4·(-178)
Δ = 9904
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9904}=\sqrt{16*619}=\sqrt{16}*\sqrt{619}=4\sqrt{619}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{619}}{2*4}=\frac{-84-4\sqrt{619}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{619}}{2*4}=\frac{-84+4\sqrt{619}}{8} $
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