100=(5x+2)(2x-1)

Solution for 100=(5x+2)(2x-1) equation:

100=(5x+2)(2x-1)

We move all terms to the left:

100-((5x+2)(2x-1))=0

We multiply parentheses ..

-((+10x^2-5x+4x-2))+100=0


We calculate terms in parentheses: -((+10x^2-5x+4x-2)), so:

(+10x^2-5x+4x-2)

We get rid of parentheses

10x^2-5x+4x-2

We add all the numbers together, and all the variables

10x^2-1x-2

Back to the equation:

-(10x^2-1x-2)


We get rid of parentheses

-10x^2+1x+2+100=0

We add all the numbers together, and all the variables

-10x^2+x+102=0

a = -10; b = 1; c = +102;
Δ = b2-4ac
Δ = 12-4·(-10)·102
Δ = 4081
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{-(1)-\sqrt{4081}}{2*-10}=\frac{-1-\sqrt{4081}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{4081}}{2*-10}=\frac{-1+\sqrt{4081}}{-20}
$