(27x^2)-4x=80

Solution for (27x^2)-4x=80 equation:

(27x^2)-4x=80

We move all terms to the left:

(27x^2)-4x-(80)=0

a = 27; b = -4; c = -80;
Δ = b2-4ac
Δ = -42-4·27·(-80)
Δ = 8656
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:

$\sqrt{\Delta}=\sqrt{8656}=\sqrt{16*541}=\sqrt{16}*\sqrt{541}=4\sqrt{541}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{541}}{2*27}=\frac{4-4\sqrt{541}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{541}}{2*27}=\frac{4+4\sqrt{541}}{54}
$