7x(x+2)=6x(x+15)

Solution for 7x(x+2)=6x(x+15) equation:

7x(x+2)=6x(x+15)

We move all terms to the left:

7x(x+2)-(6x(x+15))=0

We multiply parentheses

7x^2+14x-(6x(x+15))=0


We calculate terms in parentheses: -(6x(x+15)), so:

6x(x+15)

We multiply parentheses

6x^2+90x

Back to the equation:

-(6x^2+90x)


We get rid of parentheses

7x^2-6x^2+14x-90x=0

We add all the numbers together, and all the variables

x^2-76x=0

a = 1; b = -76; c = 0;
Δ = b2-4ac
Δ = -762-4·1·0
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-76}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+76}{2*1}=\frac{152}{2}
=76
$