(4x-3)(x)=24

Solution for (4x-3)(x)=24 equation:

(4x-3)(x)=24

We move all terms to the left:

(4x-3)(x)-(24)=0

We multiply parentheses

4x^2-3x-24=0

a = 4; b = -3; c = -24;
Δ = b2-4ac
Δ = -32-4·4·(-24)
Δ = 393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{393}}{2*4}=\frac{3-\sqrt{393}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{393}}{2*4}=\frac{3+\sqrt{393}}{8}
$