1/4x+7+2.5x=-9.5

Solution for 1/4x+7+2.5x=-9.5 equation:

1/4x+7+2.5x=-9.5

We move all terms to the left:

1/4x+7+2.5x-(-9.5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2.5x+1/4x+16.5=0

We multiply all the terms by the denominator


(2.5x)*4x+(16.5)*4x+1=0

We add all the numbers together, and all the variables

(+2.5x)*4x+(16.5)*4x+1=0

We multiply parentheses

8x^2+66x+1=0

a = 8; b = 66; c = +1;
Δ = b2-4ac
Δ = 662-4·8·1
Δ = 4324
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:

$\sqrt{\Delta}=\sqrt{4324}=\sqrt{4*1081}=\sqrt{4}*\sqrt{1081}=2\sqrt{1081}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1081}}{2*8}=\frac{-66-2\sqrt{1081}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1081}}{2*8}=\frac{-66+2\sqrt{1081}}{16}
$