(X+8)(2x)=(x+8)(10)

Solution for (X+8)(2x)=(x+8)(10) equation:

(X+8)(2X)=(X+8)(10)

We move all terms to the left:

(X+8)(2X)-((X+8)(10))=0

We multiply parentheses

2X^2+16X-((X+8)10)=0


We calculate terms in parentheses: -((X+8)10), so:

(X+8)10

We multiply parentheses

10X+80

Back to the equation:

-(10X+80)


We get rid of parentheses

2X^2+16X-10X-80=0

We add all the numbers together, and all the variables

2X^2+6X-80=0

a = 2; b = 6; c = -80;
Δ = b2-4ac
Δ = 62-4·2·(-80)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-26}{2*2}=\frac{-32}{4}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+26}{2*2}=\frac{20}{4}
=5
$