0=4x^2+50x+152

Solution for 0=4x^2+50x+152 equation:

0=4x^2+50x+152

We move all terms to the left:

0-(4x^2+50x+152)=0

We add all the numbers together, and all the variables

-(4x^2+50x+152)=0

We get rid of parentheses

-4x^2-50x-152=0

a = -4; b = -50; c = -152;
Δ = b2-4ac
Δ = -502-4·(-4)·(-152)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{17}}{2*-4}=\frac{50-2\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{17}}{2*-4}=\frac{50+2\sqrt{17}}{-8}
$