8c^2-42c+27=0

Solution for 8c^2-42c+27=0 equation:

8c^2-42c+27=0

a = 8; b = -42; c = +27;
Δ = b2-4ac
Δ = -422-4·8·27
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-30}{2*8}=\frac{12}{16}
=3/4
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+30}{2*8}=\frac{72}{16}
=4+1/2
$