12x^2=59x+14

Solution for 12x^2=59x+14 equation:

12x^2=59x+14

We move all terms to the left:

12x^2-(59x+14)=0

We get rid of parentheses

12x^2-59x-14=0

a = 12; b = -59; c = -14;
Δ = b2-4ac
Δ = -592-4·12·(-14)
Δ = 4153
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{-(-59)-\sqrt{4153}}{2*12}=\frac{59-\sqrt{4153}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{4153}}{2*12}=\frac{59+\sqrt{4153}}{24}
$