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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+X^2-5X+2X-10)-4X=0

We get rid of parentheses

X^2-5X+2X-4X-10=0

We add all the numbers together, and all the variables

X^2-7X-10=0

a = 1; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·1·(-10)
Δ = 89
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{-(-7)-\sqrt{89}}{2*1}=\frac{7-\sqrt{89}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{89}}{2*1}=\frac{7+\sqrt{89}}{2}
$