(4x+10)(14x+3)=157

Solution for (4x+10)(14x+3)=157 equation:

(4x+10)(14x+3)=157

We move all terms to the left:

(4x+10)(14x+3)-(157)=0

We multiply parentheses ..

(+56x^2+12x+140x+30)-157=0

We get rid of parentheses

56x^2+12x+140x+30-157=0

We add all the numbers together, and all the variables

56x^2+152x-127=0

a = 56; b = 152; c = -127;
Δ = b2-4ac
Δ = 1522-4·56·(-127)
Δ = 51552
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{51552}=\sqrt{144*358}=\sqrt{144}*\sqrt{358}=12\sqrt{358}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(152)-12\sqrt{358}}{2*56}=\frac{-152-12\sqrt{358}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(152)+12\sqrt{358}}{2*56}=\frac{-152+12\sqrt{358}}{112}
$