120=x(4x-3)

Solution for 120=x(4x-3) equation:

120=x(4x-3)

We move all terms to the left:

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


We calculate terms in parentheses: -(x(4x-3)), so:

x(4x-3)

We multiply parentheses

4x^2-3x

Back to the equation:

-(4x^2-3x)


We get rid of parentheses

-4x^2+3x+120=0

a = -4; b = 3; c = +120;
Δ = b2-4ac
Δ = 32-4·(-4)·120
Δ = 1929
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{1929}}{2*-4}=\frac{-3-\sqrt{1929}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{1929}}{2*-4}=\frac{-3+\sqrt{1929}}{-8}
$