4x^2-23x+47=32

Solution for 4x^2-23x+47=32 equation:

4x^2-23x+47=32

We move all terms to the left:

4x^2-23x+47-(32)=0

We add all the numbers together, and all the variables

4x^2-23x+15=0

a = 4; b = -23; c = +15;
Δ = b2-4ac
Δ = -232-4·4·15
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-17}{2*4}=\frac{6}{8}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+17}{2*4}=\frac{40}{8}
=5
$