4x^2+30x+50=54

Solution for 4x^2+30x+50=54 equation:

4x^2+30x+50=54

We move all terms to the left:

4x^2+30x+50-(54)=0

We add all the numbers together, and all the variables

4x^2+30x-4=0

a = 4; b = 30; c = -4;
Δ = b2-4ac
Δ = 302-4·4·(-4)
Δ = 964
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:

$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{241}}{2*4}=\frac{-30-2\sqrt{241}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{241}}{2*4}=\frac{-30+2\sqrt{241}}{8}
$