(2x+1.5)(x+1)=69

Solution for (2x+1.5)(x+1)=69 equation:

(2x+1.5)(x+1)=69

We move all terms to the left:

(2x+1.5)(x+1)-(69)=0

We multiply parentheses ..

(+2x^2+2x+1.5x+1.5)-69=0

We get rid of parentheses

2x^2+2x+1.5x+1.5-69=0

We add all the numbers together, and all the variables

2x^2+3.5x-67.5=0

a = 2; b = 3.5; c = -67.5;
Δ = b2-4ac
Δ = 3.52-4·2·(-67.5)
Δ = 552.25
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{-(3.5)-\sqrt{552.25}}{2*2}=\frac{-3.5-\sqrt{552.25}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.5)+\sqrt{552.25}}{2*2}=\frac{-3.5+\sqrt{552.25}}{4}
$