117x+525=3x(x+21)

Solution for 117x+525=3x(x+21) equation:

117x+525=3x(x+21)

We move all terms to the left:

117x+525-(3x(x+21))=0


We calculate terms in parentheses: -(3x(x+21)), so:

3x(x+21)

We multiply parentheses

3x^2+63x

Back to the equation:

-(3x^2+63x)


We get rid of parentheses

-3x^2+117x-63x+525=0

We add all the numbers together, and all the variables

-3x^2+54x+525=0

a = -3; b = 54; c = +525;
Δ = b2-4ac
Δ = 542-4·(-3)·525
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-96}{2*-3}=\frac{-150}{-6}
=+25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+96}{2*-3}=\frac{42}{-6}
=-7
$