8x-2=5(x+1)3x-7

Solution for 8x-2=5(x+1)3x-7 equation:

8x-2=5(x+1)3x-7

We move all terms to the left:

8x-2-(5(x+1)3x-7)=0


We calculate terms in parentheses: -(5(x+1)3x-7), so:

5(x+1)3x-7

We multiply parentheses

15x^2+15x-7

Back to the equation:

-(15x^2+15x-7)


We get rid of parentheses

-15x^2+8x-15x+7-2=0

We add all the numbers together, and all the variables

-15x^2-7x+5=0

a = -15; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·(-15)·5
Δ = 349
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{-(-7)-\sqrt{349}}{2*-15}=\frac{7-\sqrt{349}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{349}}{2*-15}=\frac{7+\sqrt{349}}{-30}
$