17x+14=4x2

Solution for 17x+14=4x2 equation:

17x+14=4x^2

We move all terms to the left:

17x+14-(4x^2)=0

determiningTheFunctionDomain
-4x^2+17x+14=0

a = -4; b = 17; c = +14;
Δ = b2-4ac
Δ = 172-4·(-4)·14
Δ = 513
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3\sqrt{57}}{2*-4}=\frac{-17-3\sqrt{57}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3\sqrt{57}}{2*-4}=\frac{-17+3\sqrt{57}}{-8}
$