4w-10=-2(w-7)w=

Solution for 4w-10=-2(w-7)w= equation:

4w-10=-2(w-7)w=

We move all terms to the left:

4w-10-(-2(w-7)w)=0


We calculate terms in parentheses: -(-2(w-7)w), so:

-2(w-7)w

We multiply parentheses

-2w^2+14w

Back to the equation:

-(-2w^2+14w)


We get rid of parentheses

2w^2-14w+4w-10=0

We add all the numbers together, and all the variables

2w^2-10w-10=0

a = 2; b = -10; c = -10;
Δ = b2-4ac
Δ = -102-4·2·(-10)
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{5}}{2*2}=\frac{10-6\sqrt{5}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{5}}{2*2}=\frac{10+6\sqrt{5}}{4}
$