(5x+6)(x-2)=7

Solution for (5x+6)(x-2)=7 equation:

(5x+6)(x-2)=7

We move all terms to the left:

(5x+6)(x-2)-(7)=0

We multiply parentheses ..

(+5x^2-10x+6x-12)-7=0

We get rid of parentheses

5x^2-10x+6x-12-7=0

We add all the numbers together, and all the variables

5x^2-4x-19=0

a = 5; b = -4; c = -19;
Δ = b2-4ac
Δ = -42-4·5·(-19)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6\sqrt{11}}{2*5}=\frac{4-6\sqrt{11}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{11}}{2*5}=\frac{4+6\sqrt{11}}{10}
$