.25x+7=1/3x-8

Solution for .25x+7=1/3x-8 equation:

.25x+7=1/3x-8

We move all terms to the left:

.25x+7-(1/3x-8)=0


Domain of the equation: 3x-8)!=0

x∈R


We get rid of parentheses

.25x-1/3x+8+7=0

We multiply all the terms by the denominator


(.25x)*3x+8*3x+7*3x-1=0

We add all the numbers together, and all the variables

(+.25x)*3x+8*3x+7*3x-1=0

We multiply parentheses

3x^2+8*3x+7*3x-1=0

Wy multiply elements

3x^2+24x+21x-1=0

We add all the numbers together, and all the variables

3x^2+45x-1=0

a = 3; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·3·(-1)
Δ = 2037
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2037}}{2*3}=\frac{-45-\sqrt{2037}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2037}}{2*3}=\frac{-45+\sqrt{2037}}{6}
$