12x2=9x+21

Solution for 12x2=9x+21 equation:

12x^2=9x+21

We move all terms to the left:

12x^2-(9x+21)=0

We get rid of parentheses

12x^2-9x-21=0

a = 12; b = -9; c = -21;
Δ = b2-4ac
Δ = -92-4·12·(-21)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-33}{2*12}=\frac{-24}{24}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+33}{2*12}=\frac{42}{24}
=1+3/4
$