3x+12=5x2

Solution for 3x+12=5x2 equation:

3x+12=5x^2

We move all terms to the left:

3x+12-(5x^2)=0

determiningTheFunctionDomain
-5x^2+3x+12=0

a = -5; b = 3; c = +12;
Δ = b2-4ac
Δ = 32-4·(-5)·12
Δ = 249
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{-(3)-\sqrt{249}}{2*-5}=\frac{-3-\sqrt{249}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{249}}{2*-5}=\frac{-3+\sqrt{249}}{-10}
$