2/11h+3=2h-7

Solution for 2/11h+3=2h-7 equation:

2/11h+3=2h-7

We move all terms to the left:

2/11h+3-(2h-7)=0


Domain of the equation: 11h!=0

h!=0/11

h!=0

h∈R


We get rid of parentheses

2/11h-2h+7+3=0

We multiply all the terms by the denominator


-2h*11h+7*11h+3*11h+2=0

Wy multiply elements

-22h^2+77h+33h+2=0

We add all the numbers together, and all the variables

-22h^2+110h+2=0

a = -22; b = 110; c = +2;
Δ = b2-4ac
Δ = 1102-4·(-22)·2
Δ = 12276
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:

$\sqrt{\Delta}=\sqrt{12276}=\sqrt{36*341}=\sqrt{36}*\sqrt{341}=6\sqrt{341}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-6\sqrt{341}}{2*-22}=\frac{-110-6\sqrt{341}}{-44}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+6\sqrt{341}}{2*-22}=\frac{-110+6\sqrt{341}}{-44}
$