4(x+3)=7(x+3)15x-15

Solution for 4(x+3)=7(x+3)15x-15 equation:

4(x+3)=7(x+3)15x-15

We move all terms to the left:

4(x+3)-(7(x+3)15x-15)=0

We multiply parentheses

4x-(7(x+3)15x-15)+12=0


We calculate terms in parentheses: -(7(x+3)15x-15), so:

7(x+3)15x-15

We multiply parentheses

105x^2+315x-15

Back to the equation:

-(105x^2+315x-15)


We get rid of parentheses

-105x^2+4x-315x+15+12=0

We add all the numbers together, and all the variables

-105x^2-311x+27=0

a = -105; b = -311; c = +27;
Δ = b2-4ac
Δ = -3112-4·(-105)·27
Δ = 108061
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{-(-311)-\sqrt{108061}}{2*-105}=\frac{311-\sqrt{108061}}{-210}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-311)+\sqrt{108061}}{2*-105}=\frac{311+\sqrt{108061}}{-210}
$