.75x+12=1/5x-10

Solution for .75x+12=1/5x-10 equation:

.75x+12=1/5x-10

We move all terms to the left:

.75x+12-(1/5x-10)=0


Domain of the equation: 5x-10)!=0

x∈R


We get rid of parentheses

.75x-1/5x+10+12=0

We multiply all the terms by the denominator


(.75x)*5x+10*5x+12*5x-1=0

We add all the numbers together, and all the variables

(+.75x)*5x+10*5x+12*5x-1=0

We multiply parentheses

5x^2+10*5x+12*5x-1=0

Wy multiply elements

5x^2+50x+60x-1=0

We add all the numbers together, and all the variables

5x^2+110x-1=0

a = 5; b = 110; c = -1;
Δ = b2-4ac
Δ = 1102-4·5·(-1)
Δ = 12120
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:

$\sqrt{\Delta}=\sqrt{12120}=\sqrt{4*3030}=\sqrt{4}*\sqrt{3030}=2\sqrt{3030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-2\sqrt{3030}}{2*5}=\frac{-110-2\sqrt{3030}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+2\sqrt{3030}}{2*5}=\frac{-110+2\sqrt{3030}}{10}
$