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

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

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

We move all terms to the left:

(2x+7)(x-3)-(-4)=0

We add all the numbers together, and all the variables

(2x+7)(x-3)+4=0

We multiply parentheses ..

(+2x^2-6x+7x-21)+4=0

We get rid of parentheses

2x^2-6x+7x-21+4=0

We add all the numbers together, and all the variables

2x^2+x-17=0

a = 2; b = 1; c = -17;
Δ = b2-4ac
Δ = 12-4·2·(-17)
Δ = 137
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{-(1)-\sqrt{137}}{2*2}=\frac{-1-\sqrt{137}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{137}}{2*2}=\frac{-1+\sqrt{137}}{4}
$