2h=h(h-6)=7

Solution for 2h=h(h-6)=7 equation:

2h=h(h-6)=7

We move all terms to the left:

2h-(h(h-6))=0


We calculate terms in parentheses: -(h(h-6)), so:

h(h-6)

We multiply parentheses

h^2-6h

Back to the equation:

-(h^2-6h)


We get rid of parentheses

-h^2+2h+6h=0

We add all the numbers together, and all the variables

-1h^2+8h=0

a = -1; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-1)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-1}=\frac{-16}{-2}
=+8
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-1}=\frac{0}{-2}
=0
$