-5(3x-4)=-29/8x

Solution for -5(3x-4)=-29/8x equation:

-5(3x-4)=-29/8x

We move all terms to the left:

-5(3x-4)-(-29/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We multiply parentheses

-15x-(-29/8x)+20=0

We get rid of parentheses

-15x+29/8x+20=0

We multiply all the terms by the denominator


-15x*8x+20*8x+29=0

Wy multiply elements

-120x^2+160x+29=0

a = -120; b = 160; c = +29;
Δ = b2-4ac
Δ = 1602-4·(-120)·29
Δ = 39520
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:

$\sqrt{\Delta}=\sqrt{39520}=\sqrt{16*2470}=\sqrt{16}*\sqrt{2470}=4\sqrt{2470}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-4\sqrt{2470}}{2*-120}=\frac{-160-4\sqrt{2470}}{-240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+4\sqrt{2470}}{2*-120}=\frac{-160+4\sqrt{2470}}{-240}
$