(2x+1)(4-x)=10

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

(2x+1)(4-x)=10

We move all terms to the left:

(2x+1)(4-x)-(10)=0

We add all the numbers together, and all the variables

(2x+1)(-1x+4)-10=0

We multiply parentheses ..

(-2x^2+8x-1x+4)-10=0

We get rid of parentheses

-2x^2+8x-1x+4-10=0

We add all the numbers together, and all the variables

-2x^2+7x-6=0

a = -2; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·(-2)·(-6)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*-2}=\frac{-6}{-4}
=1+1/2
$