2x2-5x=27

Solution for 2x2-5x=27 equation:

2x^2-5x=27

We move all terms to the left:

2x^2-5x-(27)=0

a = 2; b = -5; c = -27;
Δ = b2-4ac
Δ = -52-4·2·(-27)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{241}}{2*2}=\frac{5-\sqrt{241}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{241}}{2*2}=\frac{5+\sqrt{241}}{4}
$