-4x^2+21x=x+23

Solution for -4x^2+21x=x+23 equation:

-4x^2+21x=x+23

We move all terms to the left:

-4x^2+21x-(x+23)=0

We get rid of parentheses

-4x^2+21x-x-23=0

We add all the numbers together, and all the variables

-4x^2+20x-23=0

a = -4; b = 20; c = -23;
Δ = b2-4ac
Δ = 202-4·(-4)·(-23)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{2}}{2*-4}=\frac{-20-4\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{2}}{2*-4}=\frac{-20+4\sqrt{2}}{-8}
$