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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-19x+21=0

a = 4; b = -19; c = +21;
Δ = b2-4ac
Δ = -192-4·4·21
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-5}{2*4}=\frac{14}{8}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+5}{2*4}=\frac{24}{8}
=3
$