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

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

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

We move all terms to the left:

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

We multiply parentheses

5x^2-25x-(4(x+5))=0


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

4(x+5)

We multiply parentheses

4x+20

Back to the equation:

-(4x+20)


We get rid of parentheses

5x^2-25x-4x-20=0

We add all the numbers together, and all the variables

5x^2-29x-20=0

a = 5; b = -29; c = -20;
Δ = b2-4ac
Δ = -292-4·5·(-20)
Δ = 1241
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{-(-29)-\sqrt{1241}}{2*5}=\frac{29-\sqrt{1241}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{1241}}{2*5}=\frac{29+\sqrt{1241}}{10}
$