-3/4(x-7)+10x=1/5-6(2-x)+1

Solution for -3/4(x-7)+10x=1/5-6(2-x)+1 equation:

-3/4(x-7)+10x=1/5-6(2-x)+1

We move all terms to the left:

-3/4(x-7)+10x-(1/5-6(2-x)+1)=0


Domain of the equation: 4(x-7)!=0

x∈R



Domain of the equation: 5-6(2-x)+1)!=0

We move all terms containing x to the left, all other terms to the right

-6(2-x)+1)!=-5

x∈R


We add all the numbers together, and all the variables

-3/4(x-7)+10x-(1/5-6(-1x+2)+1)=0

We add all the numbers together, and all the variables

10x-3/4(x-7)-(1/5-6(-1x+2)+1)=0

We calculate fractions


10x+(6x-12)/(26x-152)+(-4xx/(26x-152)=0


We calculate terms in parentheses: +(-4xx/(26x-152), so:

-4xx/(26x-152

We multiply all the terms by the denominator


-4xx

Back to the equation:

+(-4xx)


We get rid of parentheses

10x+(6x-12)/(26x-152)-4xx=0

We multiply all the terms by the denominator


10x*(26x-152)+(6x-12)-4xx*(26x-152)=0

We multiply parentheses

260x^2-104x^2-1520x+(6x-12)+608x=0

We get rid of parentheses

260x^2-104x^2-1520x+6x+608x-12=0

We add all the numbers together, and all the variables

156x^2-906x-12=0

a = 156; b = -906; c = -12;
Δ = b2-4ac
Δ = -9062-4·156·(-12)
Δ = 828324
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:

$\sqrt{\Delta}=\sqrt{828324}=\sqrt{36*23009}=\sqrt{36}*\sqrt{23009}=6\sqrt{23009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-906)-6\sqrt{23009}}{2*156}=\frac{906-6\sqrt{23009}}{312}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-906)+6\sqrt{23009}}{2*156}=\frac{906+6\sqrt{23009}}{312}
$