1/2x+5(1/4x-14)=-63

Solution for 1/2x+5(1/4x-14)=-63 equation:

1/2x+5(1/4x-14)=-63

We move all terms to the left:

1/2x+5(1/4x-14)-(-63)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-14)!=0

x∈R


We add all the numbers together, and all the variables

1/2x+5(1/4x-14)+63=0

We multiply parentheses

1/2x+5x-70+63=0

We multiply all the terms by the denominator


5x*2x-70*2x+63*2x+1=0

Wy multiply elements

10x^2-140x+126x+1=0

We add all the numbers together, and all the variables

10x^2-14x+1=0

a = 10; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·10·1
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{39}}{2*10}=\frac{14-2\sqrt{39}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{39}}{2*10}=\frac{14+2\sqrt{39}}{20}
$