3*x^2+15*(x+4)=14*x*(x+4)

Solution for 3*x^2+15*(x+4)=14*x*(x+4) equation:

3x^2+15(x+4)=14x(x+4)

We move all terms to the left:

3x^2+15(x+4)-(14x(x+4))=0

We multiply parentheses

3x^2+15x-(14x(x+4))+60=0


We calculate terms in parentheses: -(14x(x+4)), so:

14x(x+4)

We multiply parentheses

14x^2+56x

Back to the equation:

-(14x^2+56x)


We get rid of parentheses

3x^2-14x^2+15x-56x+60=0

We add all the numbers together, and all the variables

-11x^2-41x+60=0

a = -11; b = -41; c = +60;
Δ = b2-4ac
Δ = -412-4·(-11)·60
Δ = 4321
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{-(-41)-\sqrt{4321}}{2*-11}=\frac{41-\sqrt{4321}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{4321}}{2*-11}=\frac{41+\sqrt{4321}}{-22}
$