X=(6x+10)(6x-5)

Solution for X=(6x+10)(6x-5) equation:

X=(6X+10)(6X-5)

We move all terms to the left:

X-((6X+10)(6X-5))=0

We multiply parentheses ..

-((+36X^2-30X+60X-50))+X=0


We calculate terms in parentheses: -((+36X^2-30X+60X-50)), so:

(+36X^2-30X+60X-50)

We get rid of parentheses

36X^2-30X+60X-50

We add all the numbers together, and all the variables

36X^2+30X-50

Back to the equation:

-(36X^2+30X-50)


We add all the numbers together, and all the variables

X-(36X^2+30X-50)=0

We get rid of parentheses

-36X^2+X-30X+50=0

We add all the numbers together, and all the variables

-36X^2-29X+50=0

a = -36; b = -29; c = +50;
Δ = b2-4ac
Δ = -292-4·(-36)·50
Δ = 8041
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{-(-29)-\sqrt{8041}}{2*-36}=\frac{29-\sqrt{8041}}{-72}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{8041}}{2*-36}=\frac{29+\sqrt{8041}}{-72}
$