-5(3+7x)+1/2x-8=-37

Solution for -5(3+7x)+1/2x-8=-37 equation:

-5(3+7x)+1/2x-8=-37

We move all terms to the left:

-5(3+7x)+1/2x-8-(-37)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-5(7x+3)+1/2x-8-(-37)=0

We add all the numbers together, and all the variables

-5(7x+3)+1/2x+29=0

We multiply parentheses

-35x+1/2x-15+29=0

We multiply all the terms by the denominator


-35x*2x-15*2x+29*2x+1=0

Wy multiply elements

-70x^2-30x+58x+1=0

We add all the numbers together, and all the variables

-70x^2+28x+1=0

a = -70; b = 28; c = +1;
Δ = b2-4ac
Δ = 282-4·(-70)·1
Δ = 1064
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:

$\sqrt{\Delta}=\sqrt{1064}=\sqrt{4*266}=\sqrt{4}*\sqrt{266}=2\sqrt{266}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{266}}{2*-70}=\frac{-28-2\sqrt{266}}{-140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{266}}{2*-70}=\frac{-28+2\sqrt{266}}{-140}
$