(2X-10)x-3=5(3x+15)

Solution for (2X-10)x-3=5(3x+15) equation:

(2X-10)X-3=5(3X+15)

We move all terms to the left:

(2X-10)X-3-(5(3X+15))=0

We multiply parentheses

2X^2-10X-(5(3X+15))-3=0


We calculate terms in parentheses: -(5(3X+15)), so:

5(3X+15)

We multiply parentheses

15X+75

Back to the equation:

-(15X+75)


We get rid of parentheses

2X^2-10X-15X-75-3=0

We add all the numbers together, and all the variables

2X^2-25X-78=0

a = 2; b = -25; c = -78;
Δ = b2-4ac
Δ = -252-4·2·(-78)
Δ = 1249
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{-(-25)-\sqrt{1249}}{2*2}=\frac{25-\sqrt{1249}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{1249}}{2*2}=\frac{25+\sqrt{1249}}{4}
$