X=(5x-7)(3x+5)

Solution for X=(5x-7)(3x+5) equation:

X=(5X-7)(3X+5)

We move all terms to the left:

X-((5X-7)(3X+5))=0

We multiply parentheses ..

-((+15X^2+25X-21X-35))+X=0


We calculate terms in parentheses: -((+15X^2+25X-21X-35)), so:

(+15X^2+25X-21X-35)

We get rid of parentheses

15X^2+25X-21X-35

We add all the numbers together, and all the variables

15X^2+4X-35

Back to the equation:

-(15X^2+4X-35)


We add all the numbers together, and all the variables

X-(15X^2+4X-35)=0

We get rid of parentheses

-15X^2+X-4X+35=0

We add all the numbers together, and all the variables

-15X^2-3X+35=0

a = -15; b = -3; c = +35;
Δ = b2-4ac
Δ = -32-4·(-15)·35
Δ = 2109
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{-(-3)-\sqrt{2109}}{2*-15}=\frac{3-\sqrt{2109}}{-30}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{2109}}{2*-15}=\frac{3+\sqrt{2109}}{-30}
$