-3-7x=-1/2x+62

Solution for -3-7x=-1/2x+62 equation:

-3-7x=-1/2x+62

We move all terms to the left:

-3-7x-(-1/2x+62)=0


Domain of the equation: 2x+62)!=0

x∈R


We get rid of parentheses

-7x+1/2x-62-3=0

We multiply all the terms by the denominator


-7x*2x-62*2x-3*2x+1=0

Wy multiply elements

-14x^2-124x-6x+1=0

We add all the numbers together, and all the variables

-14x^2-130x+1=0

a = -14; b = -130; c = +1;
Δ = b2-4ac
Δ = -1302-4·(-14)·1
Δ = 16956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16956}=\sqrt{36*471}=\sqrt{36}*\sqrt{471}=6\sqrt{471}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-6\sqrt{471}}{2*-14}=\frac{130-6\sqrt{471}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+6\sqrt{471}}{2*-14}=\frac{130+6\sqrt{471}}{-28}
$