2x+5(3x2)=3x+2(4+x)+52

Solution for 2x+5(3x2)=3x+2(4+x)+52 equation:

2x+5(3x^2)=3x+2(4+x)+52

We move all terms to the left:

2x+5(3x^2)-(3x+2(4+x)+52)=0

determiningTheFunctionDomain
53x^2+2x-(3x+2(4+x)+52)=0

We add all the numbers together, and all the variables

53x^2+2x-(3x+2(x+4)+52)=0


We calculate terms in parentheses: -(3x+2(x+4)+52), so:

3x+2(x+4)+52

We multiply parentheses

3x+2x+8+52

We add all the numbers together, and all the variables

5x+60

Back to the equation:

-(5x+60)


We get rid of parentheses

53x^2+2x-5x-60=0

We add all the numbers together, and all the variables

53x^2-3x-60=0

a = 53; b = -3; c = -60;
Δ = b2-4ac
Δ = -32-4·53·(-60)
Δ = 12729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{12729}}{2*53}=\frac{3-\sqrt{12729}}{106}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{12729}}{2*53}=\frac{3+\sqrt{12729}}{106}
$