(5x-1)(6x+3)=(-4-8x)(5x-1)

Solution for (5x-1)(6x+3)=(-4-8x)(5x-1) equation:

(5x-1)(6x+3)=(-4-8x)(5x-1)

We move all terms to the left:

(5x-1)(6x+3)-((-4-8x)(5x-1))=0

We add all the numbers together, and all the variables

(5x-1)(6x+3)-((-8x-4)(5x-1))=0

We multiply parentheses ..

(+30x^2+15x-6x-3)-((-8x-4)(5x-1))=0


We calculate terms in parentheses: -((-8x-4)(5x-1)), so:

(-8x-4)(5x-1)

We multiply parentheses ..

(-40x^2+8x-20x+4)

We get rid of parentheses

-40x^2+8x-20x+4

We add all the numbers together, and all the variables

-40x^2-12x+4

Back to the equation:

-(-40x^2-12x+4)


We get rid of parentheses

30x^2+40x^2+15x-6x+12x-3-4=0

We add all the numbers together, and all the variables

70x^2+21x-7=0

a = 70; b = 21; c = -7;
Δ = b2-4ac
Δ = 212-4·70·(-7)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-49}{2*70}=\frac{-70}{140}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+49}{2*70}=\frac{28}{140}
=1/5
$