4x^2+3x-17=23-24x

Solution for 4x^2+3x-17=23-24x equation:

4x^2+3x-17=23-24x

We move all terms to the left:

4x^2+3x-17-(23-24x)=0

We add all the numbers together, and all the variables

4x^2+3x-(-24x+23)-17=0

We get rid of parentheses

4x^2+3x+24x-23-17=0

We add all the numbers together, and all the variables

4x^2+27x-40=0

a = 4; b = 27; c = -40;
Δ = b2-4ac
Δ = 272-4·4·(-40)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-37}{2*4}=\frac{-64}{8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+37}{2*4}=\frac{10}{8}
=1+1/4
$