7x(4x+5)=6x-(8x+-6)

Solution for 7x(4x+5)=6x-(8x+-6) equation:

7x(4x+5)=6x-(8x+-6)

We move all terms to the left:

7x(4x+5)-(6x-(8x+-6))=0

We add all the numbers together, and all the variables

7x(4x+5)-(6x-(8x-6))=0

We multiply parentheses

28x^2+35x-(6x-(8x-6))=0


We calculate terms in parentheses: -(6x-(8x-6)), so:

6x-(8x-6)

We get rid of parentheses

6x-8x+6

We add all the numbers together, and all the variables

-2x+6

Back to the equation:

-(-2x+6)


We get rid of parentheses

28x^2+35x+2x-6=0

We add all the numbers together, and all the variables

28x^2+37x-6=0

a = 28; b = 37; c = -6;
Δ = b2-4ac
Δ = 372-4·28·(-6)
Δ = 2041
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{-(37)-\sqrt{2041}}{2*28}=\frac{-37-\sqrt{2041}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{2041}}{2*28}=\frac{-37+\sqrt{2041}}{56}
$