(2/3)(4x+7.5)=4x

Solution for (2/3)(4x+7.5)=4x equation:

(2/3)(4x+7.5)=4x

We move all terms to the left:

(2/3)(4x+7.5)-(4x)=0


Domain of the equation: 3)(4x+7.5)!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)(4x+7.5)-4x=0

We add all the numbers together, and all the variables

-4x+(+2/3)(4x+7.5)=0

We multiply parentheses ..

(+8x^2+2/3*7.5)-4x=0

We multiply all the terms by the denominator


(+8x^2+2-4x*3*7.5)=0

We get rid of parentheses

8x^2-4x*3*7.5+2=0

Wy multiply elements

8x^2-90x*7+2=0

Wy multiply elements

8x^2-630x+2=0

a = 8; b = -630; c = +2;
Δ = b2-4ac
Δ = -6302-4·8·2
Δ = 396836
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:

$\sqrt{\Delta}=\sqrt{396836}=\sqrt{4*99209}=\sqrt{4}*\sqrt{99209}=2\sqrt{99209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99209}}{2*8}=\frac{630-2\sqrt{99209}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99209}}{2*8}=\frac{630+2\sqrt{99209}}{16}
$