4x(2x-1)-2(x-5)=5(X+1)+3

Solution for 4x(2x-1)-2(x-5)=5(X+1)+3 equation:

4x(2x-1)-2(x-5)=5(x+1)+3

We move all terms to the left:

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

We multiply parentheses

8x^2-4x-2x-(5(x+1)+3)+10=0


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

5(x+1)+3

We multiply parentheses

5x+5+3

We add all the numbers together, and all the variables

5x+8

Back to the equation:

-(5x+8)


We add all the numbers together, and all the variables

8x^2-6x-(5x+8)+10=0

We get rid of parentheses

8x^2-6x-5x-8+10=0

We add all the numbers together, and all the variables

8x^2-11x+2=0

a = 8; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·8·2
Δ = 57
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{-(-11)-\sqrt{57}}{2*8}=\frac{11-\sqrt{57}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{57}}{2*8}=\frac{11+\sqrt{57}}{16}
$