(10x-24)(7x-18)=(5x+2)

Solution for (10x-24)(7x-18)=(5x+2) equation:

(10x-24)(7x-18)=(5x+2)

We move all terms to the left:

(10x-24)(7x-18)-((5x+2))=0

We multiply parentheses ..

(+70x^2-180x-168x+432)-((5x+2))=0


We calculate terms in parentheses: -((5x+2)), so:

(5x+2)

We get rid of parentheses

5x+2

Back to the equation:

-(5x+2)


We get rid of parentheses

70x^2-180x-168x-5x+432-2=0

We add all the numbers together, and all the variables

70x^2-353x+430=0

a = 70; b = -353; c = +430;
Δ = b2-4ac
Δ = -3532-4·70·430
Δ = 4209
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{-(-353)-\sqrt{4209}}{2*70}=\frac{353-\sqrt{4209}}{140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-353)+\sqrt{4209}}{2*70}=\frac{353+\sqrt{4209}}{140}
$