4x^2-23x+13=-3x+4

Solution for 4x^2-23x+13=-3x+4 equation:

4x^2-23x+13=-3x+4

We move all terms to the left:

4x^2-23x+13-(-3x+4)=0

We get rid of parentheses

4x^2-23x+3x-4+13=0

We add all the numbers together, and all the variables

4x^2-20x+9=0

a = 4; b = -20; c = +9;
Δ = b2-4ac
Δ = -202-4·4·9
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16}{2*4}=\frac{4}{8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16}{2*4}=\frac{36}{8}
=4+1/2
$