X=5(2x-5)(5x+4)

Solution for X=5(2x-5)(5x+4) equation:

X=5(2X-5)(5X+4)

We move all terms to the left:

X-(5(2X-5)(5X+4))=0

We multiply parentheses ..

-(5(+10X^2+8X-25X-20))+X=0


We calculate terms in parentheses: -(5(+10X^2+8X-25X-20)), so:

5(+10X^2+8X-25X-20)

We multiply parentheses

50X^2+40X-125X-100

We add all the numbers together, and all the variables

50X^2-85X-100

Back to the equation:

-(50X^2-85X-100)


We add all the numbers together, and all the variables

X-(50X^2-85X-100)=0

We get rid of parentheses

-50X^2+X+85X+100=0

We add all the numbers together, and all the variables

-50X^2+86X+100=0

a = -50; b = 86; c = +100;
Δ = b2-4ac
Δ = 862-4·(-50)·100
Δ = 27396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{27396}=\sqrt{36*761}=\sqrt{36}*\sqrt{761}=6\sqrt{761}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-6\sqrt{761}}{2*-50}=\frac{-86-6\sqrt{761}}{-100}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+6\sqrt{761}}{2*-50}=\frac{-86+6\sqrt{761}}{-100}
$