(3x-14)(2x+15)=(x-7)

Solution for (3x-14)(2x+15)=(x-7) equation:

(3x-14)(2x+15)=(x-7)

We move all terms to the left:

(3x-14)(2x+15)-((x-7))=0

We multiply parentheses ..

(+6x^2+45x-28x-210)-((x-7))=0


We calculate terms in parentheses: -((x-7)), so:

(x-7)

We get rid of parentheses

x-7

Back to the equation:

-(x-7)


We get rid of parentheses

6x^2+45x-28x-x-210+7=0

We add all the numbers together, and all the variables

6x^2+16x-203=0

a = 6; b = 16; c = -203;
Δ = b2-4ac
Δ = 162-4·6·(-203)
Δ = 5128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5128}=\sqrt{4*1282}=\sqrt{4}*\sqrt{1282}=2\sqrt{1282}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{1282}}{2*6}=\frac{-16-2\sqrt{1282}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{1282}}{2*6}=\frac{-16+2\sqrt{1282}}{12}
$