(4x+7)=12x2+21x

Solution for (4x+7)=12x2+21x equation:

(4x+7)=12x^2+21x

We move all terms to the left:

(4x+7)-(12x^2+21x)=0

We get rid of parentheses

-12x^2+4x-21x+7=0

We add all the numbers together, and all the variables

-12x^2-17x+7=0

a = -12; b = -17; c = +7;
Δ = b2-4ac
Δ = -172-4·(-12)·7
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-25}{2*-12}=\frac{-8}{-24}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+25}{2*-12}=\frac{42}{-24}
=-1+3/4
$