4/5(15+20)-7x=5/6(12x-24)+6

Solution for 4/5(15+20)-7x=5/6(12x-24)+6 equation:

4/5(15+20)-7x=5/6(12x-24)+6

We move all terms to the left:

4/5(15+20)-7x-(5/6(12x-24)+6)=0


Domain of the equation: 6(12x-24)+6)!=0

x∈R


We add all the numbers together, and all the variables

-7x-(5/6(12x-24)+6)+4/535=0

We calculate fractions


-7x+()/(72x-144)+(24x1/(72x-144)=0


We calculate terms in parentheses: +(24x1/(72x-144), so:

24x1/(72x-144

We multiply all the terms by the denominator


24x1

We add all the numbers together, and all the variables

24x

Back to the equation:

+(24x)


We add all the numbers together, and all the variables

17x+()/(72x-144)=0

We multiply all the terms by the denominator


17x*(72x-144)+()=0

We add all the numbers together, and all the variables

17x*(72x-144)=0

We multiply parentheses

1224x^2-2448x=0

a = 1224; b = -2448; c = 0;
Δ = b2-4ac
Δ = -24482-4·1224·0
Δ = 5992704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5992704}=2448$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2448)-2448}{2*1224}=\frac{0}{2448}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2448)+2448}{2*1224}=\frac{4896}{2448}
=2
$