8x(6x-7)=10X(-2x+3)

Solution for 8x(6x-7)=10X(-2x+3) equation:

8x(6x-7)=10x(-2x+3)

We move all terms to the left:

8x(6x-7)-(10x(-2x+3))=0

We multiply parentheses

48x^2-56x-(10x(-2x+3))=0


We calculate terms in parentheses: -(10x(-2x+3)), so:

10x(-2x+3)

We multiply parentheses

-20x^2+30x

Back to the equation:

-(-20x^2+30x)


We get rid of parentheses

48x^2+20x^2-30x-56x=0

We add all the numbers together, and all the variables

68x^2-86x=0

a = 68; b = -86; c = 0;
Δ = b2-4ac
Δ = -862-4·68·0
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-86}{2*68}=\frac{0}{136}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+86}{2*68}=\frac{172}{136}
=1+9/34
$