(2x-1)*x=(4x-10)*5

Solution for (2x-1)*x=(4x-10)*5 equation:

(2x-1)*x=(4x-10)*5

We move all terms to the left:

(2x-1)*x-((4x-10)*5)=0

We multiply parentheses

2x^2-1x-((4x-10)*5)=0


We calculate terms in parentheses: -((4x-10)*5), so:

(4x-10)*5

We multiply parentheses

20x-50

Back to the equation:

-(20x-50)


We get rid of parentheses

2x^2-1x-20x+50=0

We add all the numbers together, and all the variables

2x^2-21x+50=0

a = 2; b = -21; c = +50;
Δ = b2-4ac
Δ = -212-4·2·50
Δ = 41
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{41}}{2*2}=\frac{21-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{41}}{2*2}=\frac{21+\sqrt{41}}{4}
$