18x^2-59x=14

Solution for 18x^2-59x=14 equation:

18x^2-59x=14

We move all terms to the left:

18x^2-59x-(14)=0

a = 18; b = -59; c = -14;
Δ = b2-4ac
Δ = -592-4·18·(-14)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-67}{2*18}=\frac{-8}{36}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+67}{2*18}=\frac{126}{36}
=3+1/2
$