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94x^2-705x-27=0
a = 94; b = -705; c = -27;
Δ = b2-4ac
Δ = -7052-4·94·(-27)
Δ = 507177
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{507177}=\sqrt{9*56353}=\sqrt{9}*\sqrt{56353}=3\sqrt{56353}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-705)-3\sqrt{56353}}{2*94}=\frac{705-3\sqrt{56353}}{188} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-705)+3\sqrt{56353}}{2*94}=\frac{705+3\sqrt{56353}}{188} $
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