(X-4)(4x-3)=-3

Solution for (X-4)(4x-3)=-3 equation:

(X-4)(4X-3)=-3

We move all terms to the left:

(X-4)(4X-3)-(-3)=0

We add all the numbers together, and all the variables

(X-4)(4X-3)+3=0

We multiply parentheses ..

(+4X^2-3X-16X+12)+3=0

We get rid of parentheses

4X^2-3X-16X+12+3=0

We add all the numbers together, and all the variables

4X^2-19X+15=0

a = 4; b = -19; c = +15;
Δ = b2-4ac
Δ = -192-4·4·15
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-11}{2*4}=\frac{8}{8}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+11}{2*4}=\frac{30}{8}
=3+3/4
$