(5x+7)(x+2)=35

Solution for (5x+7)(x+2)=35 equation:

(5x+7)(x+2)=35

We move all terms to the left:

(5x+7)(x+2)-(35)=0

We multiply parentheses ..

(+5x^2+10x+7x+14)-35=0

We get rid of parentheses

5x^2+10x+7x+14-35=0

We add all the numbers together, and all the variables

5x^2+17x-21=0

a = 5; b = 17; c = -21;
Δ = b2-4ac
Δ = 172-4·5·(-21)
Δ = 709
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{-(17)-\sqrt{709}}{2*5}=\frac{-17-\sqrt{709}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{709}}{2*5}=\frac{-17+\sqrt{709}}{10}
$