(3x+2)(4x+5)=7

Solution for (3x+2)(4x+5)=7 equation:

(3x+2)(4x+5)=7

We move all terms to the left:

(3x+2)(4x+5)-(7)=0

We multiply parentheses ..

(+12x^2+15x+8x+10)-7=0

We get rid of parentheses

12x^2+15x+8x+10-7=0

We add all the numbers together, and all the variables

12x^2+23x+3=0

a = 12; b = 23; c = +3;
Δ = b2-4ac
Δ = 232-4·12·3
Δ = 385
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{-(23)-\sqrt{385}}{2*12}=\frac{-23-\sqrt{385}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{385}}{2*12}=\frac{-23+\sqrt{385}}{24}
$