7x+15=2(3X+8)x

Solution for 7x+15=2(3X+8)x equation:

7x+15=2(3x+8)x

We move all terms to the left:

7x+15-(2(3x+8)x)=0


We calculate terms in parentheses: -(2(3x+8)x), so:

2(3x+8)x

We multiply parentheses

6x^2+16x

Back to the equation:

-(6x^2+16x)


We get rid of parentheses

-6x^2+7x-16x+15=0

We add all the numbers together, and all the variables

-6x^2-9x+15=0

a = -6; b = -9; c = +15;
Δ = b2-4ac
Δ = -92-4·(-6)·15
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-21}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+21}{2*-6}=\frac{30}{-12}
=-2+1/2
$