0=5x^2+32x+7

Solution for 0=5x^2+32x+7 equation:

0=5x^2+32x+7

We move all terms to the left:

0-(5x^2+32x+7)=0

We add all the numbers together, and all the variables

-(5x^2+32x+7)=0

We get rid of parentheses

-5x^2-32x-7=0

a = -5; b = -32; c = -7;
Δ = b2-4ac
Δ = -322-4·(-5)·(-7)
Δ = 884
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:

$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{221}}{2*-5}=\frac{32-2\sqrt{221}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{221}}{2*-5}=\frac{32+2\sqrt{221}}{-10}
$