5(3x-3)(4x+8)-((x-5)(2x+10))=15x^2-9x-10

Solution for 5(3x-3)(4x+8)-((x-5)(2x+10))=15x^2-9x-10 equation:

5(3x-3)(4x+8)-((x-5)(2x+10))=15x^2-9x-10

We move all terms to the left:

5(3x-3)(4x+8)-((x-5)(2x+10))-(15x^2-9x-10)=0

We get rid of parentheses

-15x^2+5(3x-3)(4x+8)-((x-5)(2x+10))+9x+10=0

We multiply parentheses ..

-15x^2+5(+12x^2+24x-12x-24)-((x-5)(2x+10))+9x+10=0


We calculate terms in parentheses: -((x-5)(2x+10)), so:

(x-5)(2x+10)

We multiply parentheses ..

(+2x^2+10x-10x-50)

We get rid of parentheses

2x^2+10x-10x-50

We add all the numbers together, and all the variables

2x^2-50

Back to the equation:

-(2x^2-50)


We add all the numbers together, and all the variables

-15x^2+5(+12x^2+24x-12x-24)+9x-(2x^2-50)+10=0

We multiply parentheses

-15x^2+60x^2+120x-60x+9x-(2x^2-50)-120+10=0

We get rid of parentheses

-15x^2+60x^2-2x^2+120x-60x+9x+50-120+10=0

We add all the numbers together, and all the variables

43x^2+69x-60=0

a = 43; b = 69; c = -60;
Δ = b2-4ac
Δ = 692-4·43·(-60)
Δ = 15081
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{-(69)-\sqrt{15081}}{2*43}=\frac{-69-\sqrt{15081}}{86}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+\sqrt{15081}}{2*43}=\frac{-69+\sqrt{15081}}{86}
$