-27x^2+105x=42

Solution for -27x^2+105x=42 equation:

-27x^2+105x=42

We move all terms to the left:

-27x^2+105x-(42)=0

a = -27; b = 105; c = -42;
Δ = b2-4ac
Δ = 1052-4·(-27)·(-42)
Δ = 6489
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:

$\sqrt{\Delta}=\sqrt{6489}=\sqrt{9*721}=\sqrt{9}*\sqrt{721}=3\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-3\sqrt{721}}{2*-27}=\frac{-105-3\sqrt{721}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+3\sqrt{721}}{2*-27}=\frac{-105+3\sqrt{721}}{-54}
$