27x^2+60x=32

Solution for 27x^2+60x=32 equation:

27x^2+60x=32

We move all terms to the left:

27x^2+60x-(32)=0

a = 27; b = 60; c = -32;
Δ = b2-4ac
Δ = 602-4·27·(-32)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-84}{2*27}=\frac{-144}{54}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+84}{2*27}=\frac{24}{54}
=4/9
$