(4m+7)(4m+7)+3(4m+7)-4=0

Solution for (4m+7)(4m+7)+3(4m+7)-4=0 equation:

(4m+7)(4m+7)+3(4m+7)-4=0

We multiply parentheses

(4m+7)(4m+7)+12m+21-4=0

We multiply parentheses ..

(+16m^2+28m+28m+49)+12m+21-4=0

We add all the numbers together, and all the variables

(+16m^2+28m+28m+49)+12m+17=0

We get rid of parentheses

16m^2+28m+28m+12m+49+17=0

We add all the numbers together, and all the variables

16m^2+68m+66=0

a = 16; b = 68; c = +66;
Δ = b2-4ac
Δ = 682-4·16·66
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-20}{2*16}=\frac{-88}{32}
=-2+3/4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+20}{2*16}=\frac{-48}{32}
=-1+1/2
$