(X-2)(x+5)+3x(x-4)=7

Solution for (X-2)(x+5)+3x(x-4)=7 equation:

(X-2)(X+5)+3X(X-4)=7

We move all terms to the left:

(X-2)(X+5)+3X(X-4)-(7)=0

We multiply parentheses

3X^2+(X-2)(X+5)-12X-7=0

We multiply parentheses ..

3X^2+(+X^2+5X-2X-10)-12X-7=0

We get rid of parentheses

3X^2+X^2+5X-2X-12X-10-7=0

We add all the numbers together, and all the variables

4X^2-9X-17=0

a = 4; b = -9; c = -17;
Δ = b2-4ac
Δ = -92-4·4·(-17)
Δ = 353
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{-(-9)-\sqrt{353}}{2*4}=\frac{9-\sqrt{353}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{353}}{2*4}=\frac{9+\sqrt{353}}{8}
$