2x(x+5)-34=4(x-1)

Solution for 2x(x+5)-34=4(x-1) equation:

2x(x+5)-34=4(x-1)

We move all terms to the left:

2x(x+5)-34-(4(x-1))=0

We multiply parentheses

2x^2+10x-(4(x-1))-34=0


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

4(x-1)

We multiply parentheses

4x-4

Back to the equation:

-(4x-4)


We get rid of parentheses

2x^2+10x-4x+4-34=0

We add all the numbers together, and all the variables

2x^2+6x-30=0

a = 2; b = 6; c = -30;
Δ = b2-4ac
Δ = 62-4·2·(-30)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{69}}{2*2}=\frac{-6-2\sqrt{69}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{69}}{2*2}=\frac{-6+2\sqrt{69}}{4}
$