4x^2+10x+54=180

Solution for 4x^2+10x+54=180 equation:

4x^2+10x+54=180

We move all terms to the left:

4x^2+10x+54-(180)=0

We add all the numbers together, and all the variables

4x^2+10x-126=0

a = 4; b = 10; c = -126;
Δ = b2-4ac
Δ = 102-4·4·(-126)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-46}{2*4}=\frac{-56}{8}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+46}{2*4}=\frac{36}{8}
=4+1/2
$