X=(4x-5)(x+7)

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

X=(4X-5)(X+7)

We move all terms to the left:

X-((4X-5)(X+7))=0

We multiply parentheses ..

-((+4X^2+28X-5X-35))+X=0


We calculate terms in parentheses: -((+4X^2+28X-5X-35)), so:

(+4X^2+28X-5X-35)

We get rid of parentheses

4X^2+28X-5X-35

We add all the numbers together, and all the variables

4X^2+23X-35

Back to the equation:

-(4X^2+23X-35)


We add all the numbers together, and all the variables

X-(4X^2+23X-35)=0

We get rid of parentheses

-4X^2+X-23X+35=0

We add all the numbers together, and all the variables

-4X^2-22X+35=0

a = -4; b = -22; c = +35;
Δ = b2-4ac
Δ = -222-4·(-4)·35
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-6\sqrt{29}}{2*-4}=\frac{22-6\sqrt{29}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+6\sqrt{29}}{2*-4}=\frac{22+6\sqrt{29}}{-8}
$