8x+4=4(2x+1)3x-10=4x-13

Solution for 8x+4=4(2x+1)3x-10=4x-13 equation:

8x+4=4(2x+1)3x-10=4x-13

We move all terms to the left:

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


We calculate terms in parentheses: -(4(2x+1)3x-10), so:

4(2x+1)3x-10

We multiply parentheses

24x^2+12x-10

Back to the equation:

-(24x^2+12x-10)


We get rid of parentheses

-24x^2+8x-12x+10+4=0

We add all the numbers together, and all the variables

-24x^2-4x+14=0

a = -24; b = -4; c = +14;
Δ = b2-4ac
Δ = -42-4·(-24)·14
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{85}}{2*-24}=\frac{4-4\sqrt{85}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{85}}{2*-24}=\frac{4+4\sqrt{85}}{-48}
$