5h-7=h(h-2)+3

Solution for 5h-7=h(h-2)+3 equation:

5h-7=h(h-2)+3

We move all terms to the left:

5h-7-(h(h-2)+3)=0


We calculate terms in parentheses: -(h(h-2)+3), so:

h(h-2)+3

We multiply parentheses

h^2-2h+3

Back to the equation:

-(h^2-2h+3)


We get rid of parentheses

-h^2+5h+2h-3-7=0

We add all the numbers together, and all the variables

-1h^2+7h-10=0

a = -1; b = 7; c = -10;
Δ = b2-4ac
Δ = 72-4·(-1)·(-10)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*-1}=\frac{-10}{-2}
=+5
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*-1}=\frac{-4}{-2}
=+2
$