x(4x-7)=5x(x+21)

Solution for x(4x-7)=5x(x+21) equation:

x(4x-7)=5x(x+21)

We move all terms to the left:

x(4x-7)-(5x(x+21))=0

We multiply parentheses

4x^2-7x-(5x(x+21))=0


We calculate terms in parentheses: -(5x(x+21)), so:

5x(x+21)

We multiply parentheses

5x^2+105x

Back to the equation:

-(5x^2+105x)


We get rid of parentheses

4x^2-5x^2-7x-105x=0

We add all the numbers together, and all the variables

-1x^2-112x=0

a = -1; b = -112; c = 0;
Δ = b2-4ac
Δ = -1122-4·(-1)·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-112}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+112}{2*-1}=\frac{224}{-2}
=-112
$