24=4x(x+4)+10(x-1)

Solution for 24=4x(x+4)+10(x-1) equation:

24=4x(x+4)+10(x-1)

We move all terms to the left:

24-(4x(x+4)+10(x-1))=0


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

4x(x+4)+10(x-1)

We multiply parentheses

4x^2+16x+10x-10

We add all the numbers together, and all the variables

4x^2+26x-10

Back to the equation:

-(4x^2+26x-10)


We get rid of parentheses

-4x^2-26x+10+24=0

We add all the numbers together, and all the variables

-4x^2-26x+34=0

a = -4; b = -26; c = +34;
Δ = b2-4ac
Δ = -262-4·(-4)·34
Δ = 1220
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:

$\sqrt{\Delta}=\sqrt{1220}=\sqrt{4*305}=\sqrt{4}*\sqrt{305}=2\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{305}}{2*-4}=\frac{26-2\sqrt{305}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{305}}{2*-4}=\frac{26+2\sqrt{305}}{-8}
$