4x^2-62x+240=182

Solution for 4x^2-62x+240=182 equation:

4x^2-62x+240=182

We move all terms to the left:

4x^2-62x+240-(182)=0

We add all the numbers together, and all the variables

4x^2-62x+58=0

a = 4; b = -62; c = +58;
Δ = b2-4ac
Δ = -622-4·4·58
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-54}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+54}{2*4}=\frac{116}{8}
=14+1/2
$