45=24x^2-6x

Solution for 45=24x^2-6x equation:

45=24x^2-6x

We move all terms to the left:

45-(24x^2-6x)=0

We get rid of parentheses

-24x^2+6x+45=0

a = -24; b = 6; c = +45;
Δ = b2-4ac
Δ = 62-4·(-24)·45
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-66}{2*-24}=\frac{-72}{-48}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+66}{2*-24}=\frac{60}{-48}
=-1+1/4
$