5(7-2h)=1/2h-3

Solution for 5(7-2h)=1/2h-3 equation:

5(7-2h)=1/2h-3

We move all terms to the left:

5(7-2h)-(1/2h-3)=0


Domain of the equation: 2h-3)!=0

h∈R


We add all the numbers together, and all the variables

5(-2h+7)-(1/2h-3)=0

We multiply parentheses

-10h-(1/2h-3)+35=0

We get rid of parentheses

-10h-1/2h+3+35=0

We multiply all the terms by the denominator


-10h*2h+3*2h+35*2h-1=0

Wy multiply elements

-20h^2+6h+70h-1=0

We add all the numbers together, and all the variables

-20h^2+76h-1=0

a = -20; b = 76; c = -1;
Δ = b2-4ac
Δ = 762-4·(-20)·(-1)
Δ = 5696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5696}=\sqrt{64*89}=\sqrt{64}*\sqrt{89}=8\sqrt{89}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-8\sqrt{89}}{2*-20}=\frac{-76-8\sqrt{89}}{-40}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+8\sqrt{89}}{2*-20}=\frac{-76+8\sqrt{89}}{-40}
$