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: 5*4x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


4x*5*4x-96*5*4x+3=0

Wy multiply elements

80x^2*4-1920x*4+3=0

Wy multiply elements

320x^2-7680x+3=0

a = 320; b = -7680; c = +3;
Δ = b2-4ac
Δ = -76802-4·320·3
Δ = 58978560
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:

$\sqrt{\Delta}=\sqrt{58978560}=\sqrt{256*230385}=\sqrt{256}*\sqrt{230385}=16\sqrt{230385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7680)-16\sqrt{230385}}{2*320}=\frac{7680-16\sqrt{230385}}{640}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7680)+16\sqrt{230385}}{2*320}=\frac{7680+16\sqrt{230385}}{640}
$