4x^2+10x+118=180

Solution for 4x^2+10x+118=180 equation:

4x^2+10x+118=180

We move all terms to the left:

4x^2+10x+118-(180)=0

We add all the numbers together, and all the variables

4x^2+10x-62=0

a = 4; b = 10; c = -62;
Δ = b2-4ac
Δ = 102-4·4·(-62)
Δ = 1092
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:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{273}}{2*4}=\frac{-10-2\sqrt{273}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{273}}{2*4}=\frac{-10+2\sqrt{273}}{8}
$