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

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

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

We move all terms to the left:

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

We multiply parentheses

8x^2-40x-(7(x+5))=0


We calculate terms in parentheses: -(7(x+5)), so:

7(x+5)

We multiply parentheses

7x+35

Back to the equation:

-(7x+35)


We get rid of parentheses

8x^2-40x-7x-35=0

We add all the numbers together, and all the variables

8x^2-47x-35=0

a = 8; b = -47; c = -35;
Δ = b2-4ac
Δ = -472-4·8·(-35)
Δ = 3329
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{-(-47)-\sqrt{3329}}{2*8}=\frac{47-\sqrt{3329}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{3329}}{2*8}=\frac{47+\sqrt{3329}}{16}
$