x^2+7x+17/4=0

Solution for x^2+7x+17/4=0 equation:

x^2+7x+17/4=0

We multiply all the terms by the denominator


x^2*4+7x*4+17=0

Wy multiply elements

4x^2+28x+17=0

a = 4; b = 28; c = +17;
Δ = b2-4ac
Δ = 282-4·4·17
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-16\sqrt{2}}{2*4}=\frac{-28-16\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+16\sqrt{2}}{2*4}=\frac{-28+16\sqrt{2}}{8}
$