5(3/4x+3)=-10-5/4x

Solution for 5(3/4x+3)=-10-5/4x equation:

5(3/4x+3)=-10-5/4x

We move all terms to the left:

5(3/4x+3)-(-10-5/4x)=0


Domain of the equation: 4x+3)!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5(3/4x+3)-(-5/4x-10)=0

We multiply parentheses

15x-(-5/4x-10)+15=0

We get rid of parentheses

15x+5/4x+10+15=0

We multiply all the terms by the denominator


15x*4x+10*4x+15*4x+5=0

Wy multiply elements

60x^2+40x+60x+5=0

We add all the numbers together, and all the variables

60x^2+100x+5=0

a = 60; b = 100; c = +5;
Δ = b2-4ac
Δ = 1002-4·60·5
Δ = 8800
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:

$\sqrt{\Delta}=\sqrt{8800}=\sqrt{400*22}=\sqrt{400}*\sqrt{22}=20\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{22}}{2*60}=\frac{-100-20\sqrt{22}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{22}}{2*60}=\frac{-100+20\sqrt{22}}{120}
$