(x+4)(x+4)+(x-1)(x-1)=157

Solution for (x+4)(x+4)+(x-1)(x-1)=157 equation:

(x+4)(x+4)+(x-1)(x-1)=157

We move all terms to the left:

(x+4)(x+4)+(x-1)(x-1)-(157)=0

We multiply parentheses ..

(+x^2+4x+4x+16)+(x-1)(x-1)-157=0

We get rid of parentheses

x^2+4x+4x+(x-1)(x-1)+16-157=0

We multiply parentheses ..

x^2+(+x^2-1x-1x+1)+4x+4x+16-157=0

We add all the numbers together, and all the variables

x^2+(+x^2-1x-1x+1)+8x-141=0

We get rid of parentheses

x^2+x^2-1x-1x+8x+1-141=0

We add all the numbers together, and all the variables

2x^2+6x-140=0

a = 2; b = 6; c = -140;
Δ = b2-4ac
Δ = 62-4·2·(-140)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-34}{2*2}=\frac{-40}{4}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+34}{2*2}=\frac{28}{4}
=7
$