12x^2-5x-4=10

Solution for 12x^2-5x-4=10 equation:

12x^2-5x-4=10

We move all terms to the left:

12x^2-5x-4-(10)=0

We add all the numbers together, and all the variables

12x^2-5x-14=0

a = 12; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·12·(-14)
Δ = 697
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{697}}{2*12}=\frac{5-\sqrt{697}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{697}}{2*12}=\frac{5+\sqrt{697}}{24}
$