5(x-3)+4x(x+3)=3(x-1)

Solution for 5(x-3)+4x(x+3)=3(x-1) equation:

5(x-3)+4x(x+3)=3(x-1)

We move all terms to the left:

5(x-3)+4x(x+3)-(3(x-1))=0

We multiply parentheses

4x^2+5x+12x-(3(x-1))-15=0


We calculate terms in parentheses: -(3(x-1)), so:

3(x-1)

We multiply parentheses

3x-3

Back to the equation:

-(3x-3)


We add all the numbers together, and all the variables

4x^2+17x-(3x-3)-15=0

We get rid of parentheses

4x^2+17x-3x+3-15=0

We add all the numbers together, and all the variables

4x^2+14x-12=0

a = 4; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·4·(-12)
Δ = 388
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{97}}{2*4}=\frac{-14-2\sqrt{97}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{97}}{2*4}=\frac{-14+2\sqrt{97}}{8}
$