4x+3/5(4x)=96

Solution for 4x+3/5(4x)=96 equation:

4x+3/5(4x)=96

We move all terms to the left:

4x+3/5(4x)-(96)=0


Domain of the equation: 54x!=0

x!=0/54

x!=0

x∈R


We multiply all the terms by the denominator


4x*54x-96*54x+3=0

Wy multiply elements

216x^2-5184x+3=0

a = 216; b = -5184; c = +3;
Δ = b2-4ac
Δ = -51842-4·216·3
Δ = 26871264
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:

$\sqrt{\Delta}=\sqrt{26871264}=\sqrt{1296*20734}=\sqrt{1296}*\sqrt{20734}=36\sqrt{20734}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5184)-36\sqrt{20734}}{2*216}=\frac{5184-36\sqrt{20734}}{432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5184)+36\sqrt{20734}}{2*216}=\frac{5184+36\sqrt{20734}}{432}
$