(2/3)(5x+7)=8x

Solution for (2/3)(5x+7)=8x equation:

(2/3)(5x+7)=8x

We move all terms to the left:

(2/3)(5x+7)-(8x)=0


Domain of the equation: 3)(5x+7)!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)(5x+7)-8x=0

We add all the numbers together, and all the variables

-8x+(+2/3)(5x+7)=0

We multiply parentheses ..

(+10x^2+2/3*7)-8x=0

We multiply all the terms by the denominator


(+10x^2+2-8x*3*7)=0

We get rid of parentheses

10x^2-8x*3*7+2=0

Wy multiply elements

10x^2-168x*7+2=0

Wy multiply elements

10x^2-1176x+2=0

a = 10; b = -1176; c = +2;
Δ = b2-4ac
Δ = -11762-4·10·2
Δ = 1382896
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:

$\sqrt{\Delta}=\sqrt{1382896}=\sqrt{16*86431}=\sqrt{16}*\sqrt{86431}=4\sqrt{86431}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1176)-4\sqrt{86431}}{2*10}=\frac{1176-4\sqrt{86431}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1176)+4\sqrt{86431}}{2*10}=\frac{1176+4\sqrt{86431}}{20}
$