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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

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

We add all the numbers together, and all the variables

-5x^2-109x+7=0

a = -5; b = -109; c = +7;
Δ = b2-4ac
Δ = -1092-4·(-5)·7
Δ = 12021
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-\sqrt{12021}}{2*-5}=\frac{109-\sqrt{12021}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+\sqrt{12021}}{2*-5}=\frac{109+\sqrt{12021}}{-10}
$