21/2+7x-12x^2=0

Solution for 21/2+7x-12x^2=0 equation:

21/2+7x-12x^2=0

We multiply all the terms by the denominator


-12x^2*2+7x*2+21=0

Wy multiply elements

-24x^2+14x+21=0

a = -24; b = 14; c = +21;
Δ = b2-4ac
Δ = 142-4·(-24)·21
Δ = 2212
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2212}=\sqrt{4*553}=\sqrt{4}*\sqrt{553}=2\sqrt{553}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{553}}{2*-24}=\frac{-14-2\sqrt{553}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{553}}{2*-24}=\frac{-14+2\sqrt{553}}{-48}
$