12x^2+5x=32

Solution for 12x^2+5x=32 equation:

12x^2+5x=32

We move all terms to the left:

12x^2+5x-(32)=0

a = 12; b = 5; c = -32;
Δ = b2-4ac
Δ = 52-4·12·(-32)
Δ = 1561
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{1561}}{2*12}=\frac{-5-\sqrt{1561}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1561}}{2*12}=\frac{-5+\sqrt{1561}}{24}
$