3x+14=5x^2

Solution for 3x+14=5x^2 equation:

3x+14=5x^2

We move all terms to the left:

3x+14-(5x^2)=0

determiningTheFunctionDomain
-5x^2+3x+14=0

a = -5; b = 3; c = +14;
Δ = b2-4ac
Δ = 32-4·(-5)·14
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-17}{2*-5}=\frac{-20}{-10}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+17}{2*-5}=\frac{14}{-10}
=-1+2/5
$