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

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

X=(6X+5)(7X-8)

We move all terms to the left:

X-((6X+5)(7X-8))=0

We multiply parentheses ..

-((+42X^2-48X+35X-40))+X=0


We calculate terms in parentheses: -((+42X^2-48X+35X-40)), so:

(+42X^2-48X+35X-40)

We get rid of parentheses

42X^2-48X+35X-40

We add all the numbers together, and all the variables

42X^2-13X-40

Back to the equation:

-(42X^2-13X-40)


We add all the numbers together, and all the variables

X-(42X^2-13X-40)=0

We get rid of parentheses

-42X^2+X+13X+40=0

We add all the numbers together, and all the variables

-42X^2+14X+40=0

a = -42; b = 14; c = +40;
Δ = b2-4ac
Δ = 142-4·(-42)·40
Δ = 6916
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:

$\sqrt{\Delta}=\sqrt{6916}=\sqrt{4*1729}=\sqrt{4}*\sqrt{1729}=2\sqrt{1729}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{1729}}{2*-42}=\frac{-14-2\sqrt{1729}}{-84}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{1729}}{2*-42}=\frac{-14+2\sqrt{1729}}{-84}
$