x+121=4x(x-5)

Solution for x+121=4x(x-5) equation:

x+121=4x(x-5)

We move all terms to the left:

x+121-(4x(x-5))=0


We calculate terms in parentheses: -(4x(x-5)), so:

4x(x-5)

We multiply parentheses

4x^2-20x

Back to the equation:

-(4x^2-20x)


We get rid of parentheses

-4x^2+x+20x+121=0

We add all the numbers together, and all the variables

-4x^2+21x+121=0

a = -4; b = 21; c = +121;
Δ = b2-4ac
Δ = 212-4·(-4)·121
Δ = 2377
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{-(21)-\sqrt{2377}}{2*-4}=\frac{-21-\sqrt{2377}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{2377}}{2*-4}=\frac{-21+\sqrt{2377}}{-8}
$