(4x+7)(2x-1)=180

Solution for (4x+7)(2x-1)=180 equation:

(4x+7)(2x-1)=180

We move all terms to the left:

(4x+7)(2x-1)-(180)=0

We multiply parentheses ..

(+8x^2-4x+14x-7)-180=0

We get rid of parentheses

8x^2-4x+14x-7-180=0

We add all the numbers together, and all the variables

8x^2+10x-187=0

a = 8; b = 10; c = -187;
Δ = b2-4ac
Δ = 102-4·8·(-187)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-78}{2*8}=\frac{-88}{16}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+78}{2*8}=\frac{68}{16}
=4+1/4
$