8x+7(2-3x)x=-6(2x+5)

Solution for 8x+7(2-3x)x=-6(2x+5) equation:

8x+7(2-3x)x=-6(2x+5)

We move all terms to the left:

8x+7(2-3x)x-(-6(2x+5))=0

We add all the numbers together, and all the variables

8x+7(-3x+2)x-(-6(2x+5))=0

We multiply parentheses

-21x^2+8x+14x-(-6(2x+5))=0


We calculate terms in parentheses: -(-6(2x+5)), so:

-6(2x+5)

We multiply parentheses

-12x-30

Back to the equation:

-(-12x-30)


We add all the numbers together, and all the variables

-21x^2+22x-(-12x-30)=0

We get rid of parentheses

-21x^2+22x+12x+30=0

We add all the numbers together, and all the variables

-21x^2+34x+30=0

a = -21; b = 34; c = +30;
Δ = b2-4ac
Δ = 342-4·(-21)·30
Δ = 3676
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:

$\sqrt{\Delta}=\sqrt{3676}=\sqrt{4*919}=\sqrt{4}*\sqrt{919}=2\sqrt{919}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{919}}{2*-21}=\frac{-34-2\sqrt{919}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{919}}{2*-21}=\frac{-34+2\sqrt{919}}{-42}
$